Harmonic coordinates (English Wikipedia)

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DeTurck & Kazdan 1981; Sabitov & Šefel 1976. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014. Sabitov, I. H.; Šefel, S. Z. (1976). "Connections between the order of smoothness of a surface and that of its metric". Siberian Mathematical Journal. 17 (4): 916–925. doi:10.1007/bf00971679. MR 0425855. S2CID 120917151. Zbl 0386.53014.
Besse 2008, p. 143; Hebey 1999, p. 13; Petersen 2016, p. 409; Sakai 1996, p. 313. Hebey, Emmanuel (1999). Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes in Mathematics. Vol. 5. Providence, RI: American Mathematical Society. doi:10.1090/cln/005. ISBN 0-9658703-4-0. MR 1688256. Zbl 0981.58006. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.
DeTurck & Kazdan 1981, Lemma 1.1. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
Besse 2008, p. 143; Petersen 2016, Lemma 11.2.5. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
DeTurck & Kazdan 1981, Lemma 1.2; Besse 2008, Proposition 5.19. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
DeTurck & Kazdan 1981, Theorem 2.1. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
DeTurck & Kazdan 1981, Theorem 4.5(b); Besse 2008, Theorem 5.20b. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
DeTurck & Kazdan 1981, Theorem 4.5(c). DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
DeTurck & Kazdan 1981, Theorem 5.2; Besse 2008, Theorem 5.26. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
Taylor 2000, Sections 3.9 & 3.10. Taylor, Michael E. (2000). Tools for PDE. Pseudodifferential operators, paradifferential operators, and layer potentials. Mathematical Surveys and Monographs. Vol. 81. Providence, RI: American Mathematical Society. doi:10.1090/surv/081. ISBN 0-8218-2633-6. MR 1766415. Zbl 0963.35211.
Bartnik 1986, Definition 2.1; Lee & Parker 1987, p. 75-76. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/s0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Bartnik 1986, Corollary 3.22; Lee & Parker 1987, Theorem 9.5. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/s0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Bartnik 1986, Theorem 4.2; Lee & Parker 1987, Theorem 9.6. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/s0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Bartnik 1986, Sections 1 & 2; Lee & Parker 1987, Theorem 9.2. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/s0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Bartnik 1986, p. 678; Lee & Parker 1987, p. 78. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/s0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Bando, Kasue & Nakajima 1989, Theorem 1.1 & Remark 1.8(2). Bando, Shigetoshi; Kasue, Atsushi; Nakajima, Hiraku (1989). "On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth". Inventiones Mathematicae. 97 (2): 313–349. Bibcode:1989InMat..97..313B. doi:10.1007/BF01389045. MR 1001844. S2CID 122863673. Zbl 0682.53045.
Bando, Kasue & Nakajima 1989, pp. 324–325. Bando, Shigetoshi; Kasue, Atsushi; Nakajima, Hiraku (1989). "On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth". Inventiones Mathematicae. 97 (2): 313–349. Bibcode:1989InMat..97..313B. doi:10.1007/BF01389045. MR 1001844. S2CID 122863673. Zbl 0682.53045.
Anderson 1990, Lemma 2.2; Hebey 1999, Definition 1.1 & Theorem 1.2. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Hebey, Emmanuel (1999). Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes in Mathematics. Vol. 5. Providence, RI: American Mathematical Society. doi:10.1090/cln/005. ISBN 0-9658703-4-0. MR 1688256. Zbl 0981.58006.
Petersen 2016, Sections 11.3.1 & 11.3.4. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Hebey 1999, Theorem 1.2; Petersen 2016, Theorem 11.4.15; Sakai 1996, Theorem A6.10. Hebey, Emmanuel (1999). Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes in Mathematics. Vol. 5. Providence, RI: American Mathematical Society. doi:10.1090/cln/005. ISBN 0-9658703-4-0. MR 1688256. Zbl 0981.58006. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.
Anderson 1990, pp. 434–435; Petersen 2016, pp. 427, 429. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Anderson 1990, Lemma 2.1; Petersen 2016, Theorem 11.3.6 and Corollaries 11.3.7 & 11.3.8; Sakai 1996, p. 313. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.
Anderson 1990, Theorem 1.1; Petersen 2016, Corollary 11.4.4; Sakai 1996, Remark A6.12. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.
Hebey 1999, Proposition 3.2, Proposition 3.3, Theorem 3.4, Theorem 3.5. Hebey, Emmanuel (1999). Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes in Mathematics. Vol. 5. Providence, RI: American Mathematical Society. doi:10.1090/cln/005. ISBN 0-9658703-4-0. MR 1688256. Zbl 0981.58006.

digizeitschriften.de

Bando, Kasue & Nakajima 1989, Theorem 1.1 & Remark 1.8(2). Bando, Shigetoshi; Kasue, Atsushi; Nakajima, Hiraku (1989). "On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth". Inventiones Mathematicae. 97 (2): 313–349. Bibcode:1989InMat..97..313B. doi:10.1007/BF01389045. MR 1001844. S2CID 122863673. Zbl 0682.53045.
Bando, Kasue & Nakajima 1989, pp. 324–325. Bando, Shigetoshi; Kasue, Atsushi; Nakajima, Hiraku (1989). "On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth". Inventiones Mathematicae. 97 (2): 313–349. Bibcode:1989InMat..97..313B. doi:10.1007/BF01389045. MR 1001844. S2CID 122863673. Zbl 0682.53045.
Anderson 1990, Lemma 2.2; Hebey 1999, Definition 1.1 & Theorem 1.2. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Hebey, Emmanuel (1999). Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes in Mathematics. Vol. 5. Providence, RI: American Mathematical Society. doi:10.1090/cln/005. ISBN 0-9658703-4-0. MR 1688256. Zbl 0981.58006.
Anderson 1990, pp. 434–435; Petersen 2016, pp. 427, 429. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Anderson 1990, Lemma 2.1; Petersen 2016, Theorem 11.3.6 and Corollaries 11.3.7 & 11.3.8; Sakai 1996, p. 313. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.
Anderson 1990, Theorem 1.1; Petersen 2016, Corollary 11.4.4; Sakai 1996, Remark A6.12. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.

doi.org

DeTurck & Kazdan 1981; Sabitov & Šefel 1976. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014. Sabitov, I. H.; Šefel, S. Z. (1976). "Connections between the order of smoothness of a surface and that of its metric". Siberian Mathematical Journal. 17 (4): 916–925. doi:10.1007/bf00971679. MR 0425855. S2CID 120917151. Zbl 0386.53014.
Besse 2008, p. 143; Hebey 1999, p. 13; Petersen 2016, p. 409; Sakai 1996, p. 313. Hebey, Emmanuel (1999). Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes in Mathematics. Vol. 5. Providence, RI: American Mathematical Society. doi:10.1090/cln/005. ISBN 0-9658703-4-0. MR 1688256. Zbl 0981.58006. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.
DeTurck & Kazdan 1981, Lemma 1.1. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
Besse 2008, p. 143; Petersen 2016, Lemma 11.2.5. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
DeTurck & Kazdan 1981, Lemma 1.2; Besse 2008, Proposition 5.19. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
DeTurck & Kazdan 1981, Theorem 2.1. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
DeTurck & Kazdan 1981, Theorem 4.5(b); Besse 2008, Theorem 5.20b. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
DeTurck & Kazdan 1981, Theorem 4.5(c). DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
DeTurck & Kazdan 1981, Theorem 5.2; Besse 2008, Theorem 5.26. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
Taylor 2000, Sections 3.9 & 3.10. Taylor, Michael E. (2000). Tools for PDE. Pseudodifferential operators, paradifferential operators, and layer potentials. Mathematical Surveys and Monographs. Vol. 81. Providence, RI: American Mathematical Society. doi:10.1090/surv/081. ISBN 0-8218-2633-6. MR 1766415. Zbl 0963.35211.
Bartnik 1986, Definition 2.1; Lee & Parker 1987, p. 75-76. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/s0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Bartnik 1986, Corollary 3.22; Lee & Parker 1987, Theorem 9.5. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/s0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Bartnik 1986, Theorem 4.2; Lee & Parker 1987, Theorem 9.6. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/s0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Bartnik 1986, Sections 1 & 2; Lee & Parker 1987, Theorem 9.2. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/s0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Bartnik 1986, p. 678; Lee & Parker 1987, p. 78. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/s0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Bando, Kasue & Nakajima 1989, Theorem 1.1 & Remark 1.8(2). Bando, Shigetoshi; Kasue, Atsushi; Nakajima, Hiraku (1989). "On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth". Inventiones Mathematicae. 97 (2): 313–349. Bibcode:1989InMat..97..313B. doi:10.1007/BF01389045. MR 1001844. S2CID 122863673. Zbl 0682.53045.
Bando, Kasue & Nakajima 1989, pp. 324–325. Bando, Shigetoshi; Kasue, Atsushi; Nakajima, Hiraku (1989). "On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth". Inventiones Mathematicae. 97 (2): 313–349. Bibcode:1989InMat..97..313B. doi:10.1007/BF01389045. MR 1001844. S2CID 122863673. Zbl 0682.53045.
Anderson 1990, Lemma 2.2; Hebey 1999, Definition 1.1 & Theorem 1.2. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Hebey, Emmanuel (1999). Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes in Mathematics. Vol. 5. Providence, RI: American Mathematical Society. doi:10.1090/cln/005. ISBN 0-9658703-4-0. MR 1688256. Zbl 0981.58006.
Petersen 2016, Sections 11.3.1 & 11.3.4. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Hebey 1999, Theorem 1.2; Petersen 2016, Theorem 11.4.15; Sakai 1996, Theorem A6.10. Hebey, Emmanuel (1999). Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes in Mathematics. Vol. 5. Providence, RI: American Mathematical Society. doi:10.1090/cln/005. ISBN 0-9658703-4-0. MR 1688256. Zbl 0981.58006. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.
Anderson 1990, pp. 434–435; Petersen 2016, pp. 427, 429. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Anderson 1990, Lemma 2.1; Petersen 2016, Theorem 11.3.6 and Corollaries 11.3.7 & 11.3.8; Sakai 1996, p. 313. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.
Anderson 1990, Theorem 1.1; Petersen 2016, Corollary 11.4.4; Sakai 1996, Remark A6.12. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.
Hebey 1999, Proposition 3.2, Proposition 3.3, Theorem 3.4, Theorem 3.5. Hebey, Emmanuel (1999). Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes in Mathematics. Vol. 5. Providence, RI: American Mathematical Society. doi:10.1090/cln/005. ISBN 0-9658703-4-0. MR 1688256. Zbl 0981.58006.

handle.net

hdl.handle.net

Einstein 1916; Lanczos 1922. Lanczos, Kornel (1922). "Ein vereinfachendes Koordinatensystem für Einsteinschen Gravitationsgleichungen". Physikalische Zeitschrift. 23: 537–539. JFM 48.1023.01.

harvard.edu

ui.adsabs.harvard.edu

Bando, Kasue & Nakajima 1989, Theorem 1.1 & Remark 1.8(2). Bando, Shigetoshi; Kasue, Atsushi; Nakajima, Hiraku (1989). "On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth". Inventiones Mathematicae. 97 (2): 313–349. Bibcode:1989InMat..97..313B. doi:10.1007/BF01389045. MR 1001844. S2CID 122863673. Zbl 0682.53045.
Bando, Kasue & Nakajima 1989, pp. 324–325. Bando, Shigetoshi; Kasue, Atsushi; Nakajima, Hiraku (1989). "On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth". Inventiones Mathematicae. 97 (2): 313–349. Bibcode:1989InMat..97..313B. doi:10.1007/BF01389045. MR 1001844. S2CID 122863673. Zbl 0682.53045.
Anderson 1990, Lemma 2.2; Hebey 1999, Definition 1.1 & Theorem 1.2. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Hebey, Emmanuel (1999). Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes in Mathematics. Vol. 5. Providence, RI: American Mathematical Society. doi:10.1090/cln/005. ISBN 0-9658703-4-0. MR 1688256. Zbl 0981.58006.
Anderson 1990, pp. 434–435; Petersen 2016, pp. 427, 429. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Anderson 1990, Lemma 2.1; Petersen 2016, Theorem 11.3.6 and Corollaries 11.3.7 & 11.3.8; Sakai 1996, p. 313. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.
Anderson 1990, Theorem 1.1; Petersen 2016, Corollary 11.4.4; Sakai 1996, Remark A6.12. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.

semanticscholar.org

api.semanticscholar.org

DeTurck & Kazdan 1981; Sabitov & Šefel 1976. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014. Sabitov, I. H.; Šefel, S. Z. (1976). "Connections between the order of smoothness of a surface and that of its metric". Siberian Mathematical Journal. 17 (4): 916–925. doi:10.1007/bf00971679. MR 0425855. S2CID 120917151. Zbl 0386.53014.
Bando, Kasue & Nakajima 1989, Theorem 1.1 & Remark 1.8(2). Bando, Shigetoshi; Kasue, Atsushi; Nakajima, Hiraku (1989). "On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth". Inventiones Mathematicae. 97 (2): 313–349. Bibcode:1989InMat..97..313B. doi:10.1007/BF01389045. MR 1001844. S2CID 122863673. Zbl 0682.53045.
Bando, Kasue & Nakajima 1989, pp. 324–325. Bando, Shigetoshi; Kasue, Atsushi; Nakajima, Hiraku (1989). "On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth". Inventiones Mathematicae. 97 (2): 313–349. Bibcode:1989InMat..97..313B. doi:10.1007/BF01389045. MR 1001844. S2CID 122863673. Zbl 0682.53045.
Anderson 1990, Lemma 2.2; Hebey 1999, Definition 1.1 & Theorem 1.2. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Hebey, Emmanuel (1999). Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes in Mathematics. Vol. 5. Providence, RI: American Mathematical Society. doi:10.1090/cln/005. ISBN 0-9658703-4-0. MR 1688256. Zbl 0981.58006.
Anderson 1990, pp. 434–435; Petersen 2016, pp. 427, 429. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Anderson 1990, Lemma 2.1; Petersen 2016, Theorem 11.3.6 and Corollaries 11.3.7 & 11.3.8; Sakai 1996, p. 313. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.
Anderson 1990, Theorem 1.1; Petersen 2016, Corollary 11.4.4; Sakai 1996, Remark A6.12. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.

zbmath.org

Einstein 1916; Lanczos 1922. Lanczos, Kornel (1922). "Ein vereinfachendes Koordinatensystem für Einsteinschen Gravitationsgleichungen". Physikalische Zeitschrift. 23: 537–539. JFM 48.1023.01.
DeTurck & Kazdan 1981; Sabitov & Šefel 1976. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014. Sabitov, I. H.; Šefel, S. Z. (1976). "Connections between the order of smoothness of a surface and that of its metric". Siberian Mathematical Journal. 17 (4): 916–925. doi:10.1007/bf00971679. MR 0425855. S2CID 120917151. Zbl 0386.53014.
Besse 2008, p. 143; Hebey 1999, p. 13; Petersen 2016, p. 409; Sakai 1996, p. 313. Hebey, Emmanuel (1999). Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes in Mathematics. Vol. 5. Providence, RI: American Mathematical Society. doi:10.1090/cln/005. ISBN 0-9658703-4-0. MR 1688256. Zbl 0981.58006. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.
DeTurck & Kazdan 1981, Lemma 1.1. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
Besse 2008, p. 143; Petersen 2016, Lemma 11.2.5. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
DeTurck & Kazdan 1981, Lemma 1.2; Besse 2008, Proposition 5.19. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
DeTurck & Kazdan 1981, Theorem 2.1. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
DeTurck & Kazdan 1981, Theorem 4.5(b); Besse 2008, Theorem 5.20b. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
DeTurck & Kazdan 1981, Theorem 4.5(c). DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
DeTurck & Kazdan 1981, Theorem 5.2; Besse 2008, Theorem 5.26. DeTurck, Dennis M.; Kazdan, Jerry L. (1981). "Some regularity theorems in Riemannian geometry". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 14 (3): 249–260. doi:10.24033/asens.1405. MR 0644518. Zbl 0486.53014.
Taylor 2000, Sections 3.9 & 3.10. Taylor, Michael E. (2000). Tools for PDE. Pseudodifferential operators, paradifferential operators, and layer potentials. Mathematical Surveys and Monographs. Vol. 81. Providence, RI: American Mathematical Society. doi:10.1090/surv/081. ISBN 0-8218-2633-6. MR 1766415. Zbl 0963.35211.
Bartnik 1986, Definition 2.1; Lee & Parker 1987, p. 75-76. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/s0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Bartnik 1986, Corollary 3.22; Lee & Parker 1987, Theorem 9.5. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/s0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Bartnik 1986, Theorem 4.2; Lee & Parker 1987, Theorem 9.6. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/s0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Bartnik 1986, Sections 1 & 2; Lee & Parker 1987, Theorem 9.2. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/s0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Bartnik 1986, p. 678; Lee & Parker 1987, p. 78. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/s0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Bando, Kasue & Nakajima 1989, Theorem 1.1 & Remark 1.8(2). Bando, Shigetoshi; Kasue, Atsushi; Nakajima, Hiraku (1989). "On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth". Inventiones Mathematicae. 97 (2): 313–349. Bibcode:1989InMat..97..313B. doi:10.1007/BF01389045. MR 1001844. S2CID 122863673. Zbl 0682.53045.
Bando, Kasue & Nakajima 1989, pp. 324–325. Bando, Shigetoshi; Kasue, Atsushi; Nakajima, Hiraku (1989). "On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth". Inventiones Mathematicae. 97 (2): 313–349. Bibcode:1989InMat..97..313B. doi:10.1007/BF01389045. MR 1001844. S2CID 122863673. Zbl 0682.53045.
Anderson 1990, Lemma 2.2; Hebey 1999, Definition 1.1 & Theorem 1.2. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Hebey, Emmanuel (1999). Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes in Mathematics. Vol. 5. Providence, RI: American Mathematical Society. doi:10.1090/cln/005. ISBN 0-9658703-4-0. MR 1688256. Zbl 0981.58006.
Petersen 2016, Sections 11.3.1 & 11.3.4. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Hebey 1999, Theorem 1.2; Petersen 2016, Theorem 11.4.15; Sakai 1996, Theorem A6.10. Hebey, Emmanuel (1999). Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes in Mathematics. Vol. 5. Providence, RI: American Mathematical Society. doi:10.1090/cln/005. ISBN 0-9658703-4-0. MR 1688256. Zbl 0981.58006. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.
Anderson 1990, pp. 434–435; Petersen 2016, pp. 427, 429. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Anderson 1990, Lemma 2.1; Petersen 2016, Theorem 11.3.6 and Corollaries 11.3.7 & 11.3.8; Sakai 1996, p. 313. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.
Anderson 1990, Theorem 1.1; Petersen 2016, Corollary 11.4.4; Sakai 1996, Remark A6.12. Anderson, Michael T. (1990). "Convergence and rigidity of manifolds under Ricci curvature bounds". Inventiones Mathematicae. 102 (2): 429–445. Bibcode:1990InMat.102..429A. doi:10.1007/bf01233434. MR 1074481. S2CID 121062092. Zbl 0711.53038. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001. Sakai, Takashi (1996). Riemannian geometry. Translations of Mathematical Monographs. Vol. 149. Providence, RI: American Mathematical Society. doi:10.1090/mmono/149. ISBN 0-8218-0284-4. MR 1390760. Zbl 0886.53002.
Hebey 1999, Proposition 3.2, Proposition 3.3, Theorem 3.4, Theorem 3.5. Hebey, Emmanuel (1999). Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes in Mathematics. Vol. 5. Providence, RI: American Mathematical Society. doi:10.1090/cln/005. ISBN 0-9658703-4-0. MR 1688256. Zbl 0981.58006.