Differential geometry of surfaces (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Differential geometry of surfaces" in English language version.

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ams.org

mathscinet.ams.org

Berger 2004; Wilson 2008; Milnor 1963. Berger, Marcel (2004), A Panoramic View of Riemannian Geometry, Springer-Verlag, ISBN 978-3-540-65317-2 Wilson, Pelham (2008), Curved Space: From Classical Geometries to Elementary Differential Geometry, Cambridge University Press, ISBN 978-0-521-71390-0 Milnor, J. (1963). Morse theory. Annals of Mathematics Studies. Vol. 51. Princeton, N.J.: Princeton University Press. MR 0163331. Zbl 0108.10401.
Milnor 1963 Milnor, J. (1963). Morse theory. Annals of Mathematics Studies. Vol. 51. Princeton, N.J.: Princeton University Press. MR 0163331. Zbl 0108.10401.

arxiv.org

Chen, Lu & Tian (2006) pointed out and corrected a missing step in the approach of Hamilton and Chow; see also Andrews & Bryan (2010). Chen, Xiuxiong; Lu, Peng; Tian, Gang (2006), "A note on uniformization of Riemann surfaces by Ricci flow", Proc. AMS, 134 (11): 3391–3393, doi:10.1090/S0002-9939-06-08360-2 Andrews, Ben; Bryan, Paul (2010), "Curvature bounds by isoperimetric comparison for normalized Ricci flow on the two-sphere", Calc. Var. Partial Differential Equations, 39 (3–4): 419–428, arXiv:0908.3606, doi:10.1007/s00526-010-0315-5, S2CID 1095459
Codá Marques, Fernando; Neves, André (2014). "Min-Max theory and the Willmore conjecture". Annals of Mathematics. 179 (2): 683–782. arXiv:1202.6036. doi:10.4007/annals.2014.179.2.6. JSTOR 24522767. S2CID 50742102.

dartmouth.edu

math.dartmouth.edu

Euler 1760 Euler, Leonhard (1760), "Recherches sur la courbure des surfaces", Mémoires de l'Académie des Sciences de Berlin, 16 (published 1767): 119–143.
Euler 1771 Euler, Leonhard (1771), "De solidis quorum superficiem in planum explicare licet", Novi Commentarii Academiae Scientiarum Petropolitanae, 16 (published 1772): 3–34.

doi.org

This follows by an argument involving a theorem of Sacks & Uhlenbeck (1981) on removable singularities of harmonic maps of finite energy. Sacks, J.; Uhlenbeck, Karen (1981), "The existence of minimal immersions of 2-spheres", Ann. of Math., 112 (1): 1–24, doi:10.2307/1971131, JSTOR 1971131
Singer & Thorpe 1967; Garsia, Adriano M. (1961), "An imbedding of closed Riemann surfaces in Euclidean space", Comment. Math. Helv., 35: 93–110, doi:10.1007/BF02567009, S2CID 120653575 Singer, Isadore M.; Thorpe, John A. (1967), Lecture Notes on Elementary Topology and Geometry, Springer-Verlag, ISBN 978-0-387-90202-9
Chow 1991 Chow, B. (1991), "The Ricci flow on a 2-sphere", J. Diff. Geom., 33 (2): 325–334, doi:10.4310/jdg/1214446319
Chen, Lu & Tian (2006) pointed out and corrected a missing step in the approach of Hamilton and Chow; see also Andrews & Bryan (2010). Chen, Xiuxiong; Lu, Peng; Tian, Gang (2006), "A note on uniformization of Riemann surfaces by Ricci flow", Proc. AMS, 134 (11): 3391–3393, doi:10.1090/S0002-9939-06-08360-2 Andrews, Ben; Bryan, Paul (2010), "Curvature bounds by isoperimetric comparison for normalized Ricci flow on the two-sphere", Calc. Var. Partial Differential Equations, 39 (3–4): 419–428, arXiv:0908.3606, doi:10.1007/s00526-010-0315-5, S2CID 1095459
Levi-Civita 1917 Levi-Civita, Tullio (1917), "Nozione di parallelismo in una varietà qualunque", Rend. Circ. Mat. Palermo, 42: 173–205, doi:10.1007/BF03014898, S2CID 122088291
Codá Marques, Fernando; Neves, André (2014). "Min-Max theory and the Willmore conjecture". Annals of Mathematics. 179 (2): 683–782. arXiv:1202.6036. doi:10.4007/annals.2014.179.2.6. JSTOR 24522767. S2CID 50742102.

jstor.org

This follows by an argument involving a theorem of Sacks & Uhlenbeck (1981) on removable singularities of harmonic maps of finite energy. Sacks, J.; Uhlenbeck, Karen (1981), "The existence of minimal immersions of 2-spheres", Ann. of Math., 112 (1): 1–24, doi:10.2307/1971131, JSTOR 1971131
Codá Marques, Fernando; Neves, André (2014). "Min-Max theory and the Willmore conjecture". Annals of Mathematics. 179 (2): 683–782. arXiv:1202.6036. doi:10.4007/annals.2014.179.2.6. JSTOR 24522767. S2CID 50742102.

ox.ac.uk

people.maths.ox.ac.uk

Hitchin 2013, p. 45 Hitchin, Nigel (2013), Geometry of Surfaces (PDF)
Hitchin 2013, p. 57 Hitchin, Nigel (2013), Geometry of Surfaces (PDF)
Hitchin 2013, pp. 57–58 Hitchin, Nigel (2013), Geometry of Surfaces (PDF)
Hitchin 2013 Hitchin, Nigel (2013), Geometry of Surfaces (PDF)

projecteuclid.org

Eisenhart 2004, pp. 228–229 Eisenhart, Luther Pfahler (2004), A Treatise on the Differential Geometry of Curves and Surfaces (reprint of the 1909 ed.), Dover Publications, Inc., ISBN 0-486-43820-1
Eisenhart 2004, pp. 241–250; do Carmo 2016, pp. 188–197. Eisenhart, Luther Pfahler (2004), A Treatise on the Differential Geometry of Curves and Surfaces (reprint of the 1909 ed.), Dover Publications, Inc., ISBN 0-486-43820-1 do Carmo, Manfredo P. (2016), Differential Geometry of Curves and Surfaces (revised & updated 2nd ed.), Mineola, NY: Dover Publications, Inc., ISBN 978-0-486-80699-0
Eisenhart 2004, pp. 61–65. Eisenhart, Luther Pfahler (2004), A Treatise on the Differential Geometry of Curves and Surfaces (reprint of the 1909 ed.), Dover Publications, Inc., ISBN 0-486-43820-1
Eisenhart 2004 Eisenhart, Luther Pfahler (2004), A Treatise on the Differential Geometry of Curves and Surfaces (reprint of the 1909 ed.), Dover Publications, Inc., ISBN 0-486-43820-1
Eisenhart 2004, pp. 250–269; do Carmo 2016, pp. 197–213. Eisenhart, Luther Pfahler (2004), A Treatise on the Differential Geometry of Curves and Surfaces (reprint of the 1909 ed.), Dover Publications, Inc., ISBN 0-486-43820-1 do Carmo, Manfredo P. (2016), Differential Geometry of Curves and Surfaces (revised & updated 2nd ed.), Mineola, NY: Dover Publications, Inc., ISBN 978-0-486-80699-0
Eisenhart 2004, pp. 270–291; O'Neill 2006, pp. 249–251; Hilbert & Cohn-Vossen 1952. Eisenhart, Luther Pfahler (2004), A Treatise on the Differential Geometry of Curves and Surfaces (reprint of the 1909 ed.), Dover Publications, Inc., ISBN 0-486-43820-1 O'Neill, Barrett (2006), Elementary Differential Geometry (revised 2nd ed.), Amsterdam: Elsevier/Academic Press, ISBN 0-12-088735-5 Hilbert, David; Cohn-Vossen, Stephan (1952), Geometry and the Imagination (2nd ed.), New York: Chelsea, ISBN 978-0-8284-1087-8
Eisenhart 2004, p. 131; Berger 2004, p. 39; do Carmo 2016, p. 248; O'Neill 2006, p. 237 Eisenhart, Luther Pfahler (2004), A Treatise on the Differential Geometry of Curves and Surfaces (reprint of the 1909 ed.), Dover Publications, Inc., ISBN 0-486-43820-1 Berger, Marcel (2004), A Panoramic View of Riemannian Geometry, Springer-Verlag, ISBN 978-3-540-65317-2 do Carmo, Manfredo P. (2016), Differential Geometry of Curves and Surfaces (revised & updated 2nd ed.), Mineola, NY: Dover Publications, Inc., ISBN 978-0-486-80699-0 O'Neill, Barrett (2006), Elementary Differential Geometry (revised 2nd ed.), Amsterdam: Elsevier/Academic Press, ISBN 0-12-088735-5
Eisenhart 2004; Taylor 1996a, pp. 472–473, Appendix C. Eisenhart, Luther Pfahler (2004), A Treatise on the Differential Geometry of Curves and Surfaces (reprint of the 1909 ed.), Dover Publications, Inc., ISBN 0-486-43820-1 Taylor, Michael E. (1996a), Partial Differential Equations II: Qualitative Studies of Linear Equations, Springer-Verlag, ISBN 978-1-4419-7051-0
Eisenhart 2004, section 88; Berger 2004. Eisenhart, Luther Pfahler (2004), A Treatise on the Differential Geometry of Curves and Surfaces (reprint of the 1909 ed.), Dover Publications, Inc., ISBN 0-486-43820-1 Berger, Marcel (2004), A Panoramic View of Riemannian Geometry, Springer-Verlag, ISBN 978-3-540-65317-2
Eisenhart 2004, p. 110. Eisenhart, Luther Pfahler (2004), A Treatise on the Differential Geometry of Curves and Surfaces (reprint of the 1909 ed.), Dover Publications, Inc., ISBN 0-486-43820-1
Eisenhart 2004; Kreyszig 1991; Berger 2004; Wilson 2008. Eisenhart, Luther Pfahler (2004), A Treatise on the Differential Geometry of Curves and Surfaces (reprint of the 1909 ed.), Dover Publications, Inc., ISBN 0-486-43820-1 Kreyszig, Erwin (1991), Differential Geometry, Dover, ISBN 978-0-486-66721-8 Berger, Marcel (2004), A Panoramic View of Riemannian Geometry, Springer-Verlag, ISBN 978-3-540-65317-2 Wilson, Pelham (2008), Curved Space: From Classical Geometries to Elementary Differential Geometry, Cambridge University Press, ISBN 978-0-521-71390-0

semanticscholar.org

api.semanticscholar.org

Singer & Thorpe 1967; Garsia, Adriano M. (1961), "An imbedding of closed Riemann surfaces in Euclidean space", Comment. Math. Helv., 35: 93–110, doi:10.1007/BF02567009, S2CID 120653575 Singer, Isadore M.; Thorpe, John A. (1967), Lecture Notes on Elementary Topology and Geometry, Springer-Verlag, ISBN 978-0-387-90202-9
Chen, Lu & Tian (2006) pointed out and corrected a missing step in the approach of Hamilton and Chow; see also Andrews & Bryan (2010). Chen, Xiuxiong; Lu, Peng; Tian, Gang (2006), "A note on uniformization of Riemann surfaces by Ricci flow", Proc. AMS, 134 (11): 3391–3393, doi:10.1090/S0002-9939-06-08360-2 Andrews, Ben; Bryan, Paul (2010), "Curvature bounds by isoperimetric comparison for normalized Ricci flow on the two-sphere", Calc. Var. Partial Differential Equations, 39 (3–4): 419–428, arXiv:0908.3606, doi:10.1007/s00526-010-0315-5, S2CID 1095459
Levi-Civita 1917 Levi-Civita, Tullio (1917), "Nozione di parallelismo in una varietà qualunque", Rend. Circ. Mat. Palermo, 42: 173–205, doi:10.1007/BF03014898, S2CID 122088291
Codá Marques, Fernando; Neves, André (2014). "Min-Max theory and the Willmore conjecture". Annals of Mathematics. 179 (2): 683–782. arXiv:1202.6036. doi:10.4007/annals.2014.179.2.6. JSTOR 24522767. S2CID 50742102.

umich.edu

quod.lib.umich.edu

Gauss 1902. Gauss, Carl Friedrich (1902), General Investigations of Curved Surfaces of 1825 and 1827, Princeton University Library translated by A.M. Hiltebeitel and J.C. Morehead; "Disquisitiones generales circa superficies curvas", Commentationes Societatis Regiae Scientiarum Gottingesis Recentiores Vol. VI (1827), pp. 99–146.
hti.umich.edu
- Darboux. Darboux, Gaston, Leçons sur la théorie générale des surfaces, Gauthier-Villars Volume I (1887), Volume II (1915) [1889], Volume III (1894), Volume IV (1896).

uni-goettingen.de

www-gdz.sub.uni-goettingen.de

Gauss 1902. Gauss, Carl Friedrich (1902), General Investigations of Curved Surfaces of 1825 and 1827, Princeton University Library translated by A.M. Hiltebeitel and J.C. Morehead; "Disquisitiones generales circa superficies curvas", Commentationes Societatis Regiae Scientiarum Gottingesis Recentiores Vol. VI (1827), pp. 99–146.

worldcat.org

search.worldcat.org

Gauss 1902. Gauss, Carl Friedrich (1902), General Investigations of Curved Surfaces of 1825 and 1827, Princeton University Library translated by A.M. Hiltebeitel and J.C. Morehead; "Disquisitiones generales circa superficies curvas", Commentationes Societatis Regiae Scientiarum Gottingesis Recentiores Vol. VI (1827), pp. 99–146.

zbmath.org

Berger 2004; Wilson 2008; Milnor 1963. Berger, Marcel (2004), A Panoramic View of Riemannian Geometry, Springer-Verlag, ISBN 978-3-540-65317-2 Wilson, Pelham (2008), Curved Space: From Classical Geometries to Elementary Differential Geometry, Cambridge University Press, ISBN 978-0-521-71390-0 Milnor, J. (1963). Morse theory. Annals of Mathematics Studies. Vol. 51. Princeton, N.J.: Princeton University Press. MR 0163331. Zbl 0108.10401.
Milnor 1963 Milnor, J. (1963). Morse theory. Annals of Mathematics Studies. Vol. 51. Princeton, N.J.: Princeton University Press. MR 0163331. Zbl 0108.10401.

zenodo.org

Levi-Civita 1917 Levi-Civita, Tullio (1917), "Nozione di parallelismo in una varietà qualunque", Rend. Circ. Mat. Palermo, 42: 173–205, doi:10.1007/BF03014898, S2CID 122088291