Carathéodory conjecture (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Carathéodory conjecture" in English language version.

refsWebsite

Global rank English rank

14doi.org

2^nd place

11semanticscholar.org

11^th place

8^th place

10arxiv.org

69^th place

59^th place

3worldcat.org

5^th place

1ams.org

451^st place

277^th place

1uni-goettingen.de

2,594^th place

2,546^th place

1gokovagt.org

low place

1harvard.edu

18^th place

17^th place

1gatech.edu

4,448^th place

2,923^rd place

ams.org (Global: 451^st place; English: 277^th place)

Struik, D. J. (1931). "Differential Geometry in the large". Bull. Amer. Math. Soc. 37 (2): 49–62. doi:10.1090/S0002-9904-1931-05094-1.

arxiv.org (Global: 69^th place; English: 59^th place)

Guilfoyle, B.; Klingenberg, W. (2008). "Proof of the Carathéodory conjecture". arXiv:0808.0851 [math.DG].
Guilfoyle, B.; Klingenberg, W. (2019). "Higher codimensional mean curvature flow of compact spacelike submanifolds". Trans. Amer. Math. Soc. 372 (9): 6263–6281. arXiv:1812.00710. doi:10.1090/tran/7766. S2CID 119253397.
Guilfoyle, B.; Klingenberg, W. (2020). "Fredholm-regularity of holomorphic discs in plane bundles over compact surfaces". Ann. Fac. Sci. Toulouse Math. Série 6. 29 (3): 565–576. arXiv:1812.00707. doi:10.5802/afst.1639. S2CID 119659239.
Guilfoyle, B.; Klingenberg, W. (2024). "Proof of the Toponogov Conjecture on complete surfaces". J. Gökova Geom. Topol. GGT. 17: 1–50. arXiv:2002.12787.
Guilfoyle, B.; Klingenberg, W. (2025). "The three obdurate conjectures of differential geometry". Math. Proc. R. Ir. Acad. 125A: 9–17. arXiv:2502.11716. doi:10.1353/mpr.2025.a968272.
Guilfoyle, B. (2020). "On Isolated Umbilic Points". Comm. Anal. Geom. 28 (8): 2005–2018. arXiv:1812.03562. doi:10.4310/CAG.2020.v28.n8.a8. S2CID 119158738.
Guilfoyle, B.; Klingenberg, W. (2023). "Roots of polynomials and umbilics of surfaces". Results in Math. 78 (6): 229–247. arXiv:2204.13163. doi:10.1007/s00025-023-02003-4. S2CID 248426964.
Guilfoyle, B.; Klingenberg, W. (2005). "An indefinite Kähler metric on the space of oriented lines". J. London Math. Soc. 72 (2): 497–509. arXiv:math/0407490. doi:10.1112/S0024610705006605. S2CID 14978450.
Guilfoyle, B.; Klingenberg, W. (2012). "An index bound for smooth umbilic points". arXiv:1207.5994 [math.DG].
Ghomi, M.; Howard, R. (2012). "Normal curvatures of asymptotically constant graphs and Carathéodory's conjecture". Proc. Amer. Math. Soc. 140 (12): 4323–4335. arXiv:1101.3031. doi:10.1090/S0002-9939-2012-11420-0. S2CID 12148752.

doi.org (Global: 2^nd place; English: 2^nd place)

Struik, D. J. (1931). "Differential Geometry in the large". Bull. Amer. Math. Soc. 37 (2): 49–62. doi:10.1090/S0002-9904-1931-05094-1.
Bol, G. (1944). "Über Nabelpunkte auf einer Eifläche". Math. Z. 49: 389–410. doi:10.1007/bf01174209. S2CID 120816230.
Klotz, Tilla (1959). "On G. Bol's proof of Carathéodory's conjecture". Commun. Pure Appl. Math. 12 (2): 277–311. doi:10.1002/cpa.3160120207.
Guilfoyle, B.; Klingenberg, W. (2019). "Higher codimensional mean curvature flow of compact spacelike submanifolds". Trans. Amer. Math. Soc. 372 (9): 6263–6281. arXiv:1812.00710. doi:10.1090/tran/7766. S2CID 119253397.
Guilfoyle, B.; Klingenberg, W. (2020). "Fredholm-regularity of holomorphic discs in plane bundles over compact surfaces". Ann. Fac. Sci. Toulouse Math. Série 6. 29 (3): 565–576. arXiv:1812.00707. doi:10.5802/afst.1639. S2CID 119659239.
Guilfoyle, B.; Klingenberg, W. (2025). "The three obdurate conjectures of differential geometry". Math. Proc. R. Ir. Acad. 125A: 9–17. arXiv:2502.11716. doi:10.1353/mpr.2025.a968272.
Guilfoyle, B. (2020). "On Isolated Umbilic Points". Comm. Anal. Geom. 28 (8): 2005–2018. arXiv:1812.03562. doi:10.4310/CAG.2020.v28.n8.a8. S2CID 119158738.
Hamburger, H. (1924). "Über Kurvennetze mit isolierten Singularitäten auf geschossenen Flächen". Math. Z. 19: 50–66. doi:10.1007/bf01181063. S2CID 121237690.
Titus, C. J. (1973). "A proof of a conjecture of Loewner and of the conjecture of Carathéodory on umbilic points". Acta Math. 131 (1–2): 43–77. doi:10.1007/BF02392036. S2CID 119377800.
Ivanov, V. V. (2002). "The Analytic Carathéodory Conjecture". Sib. Math. J. 43 (2): 251–322. Bibcode:2002SibMJ..43..251I. doi:10.1023/A:1014797105633. ISSN 0037-4474. S2CID 117115329.
Guilfoyle, B.; Klingenberg, W. (2023). "Roots of polynomials and umbilics of surfaces". Results in Math. 78 (6): 229–247. arXiv:2204.13163. doi:10.1007/s00025-023-02003-4. S2CID 248426964.
Guilfoyle, B.; Klingenberg, W. (2005). "An indefinite Kähler metric on the space of oriented lines". J. London Math. Soc. 72 (2): 497–509. arXiv:math/0407490. doi:10.1112/S0024610705006605. S2CID 14978450.
Guilfoyle, B.; Klingenberg, W. (2004). "Generalised surfaces in $R^{3}$ ". Math. Proc. R. Ir. Acad. 104A (2): 199–209. doi:10.1353/mpr.2004.0013. S2CID 118128548.
Ghomi, M.; Howard, R. (2012). "Normal curvatures of asymptotically constant graphs and Carathéodory's conjecture". Proc. Amer. Math. Soc. 140 (12): 4323–4335. arXiv:1101.3031. doi:10.1090/S0002-9939-2012-11420-0. S2CID 12148752.

gatech.edu (Global: 4,448^th place; English: 2,923^rd place)

people.math.gatech.edu

Ghomi, M. (2017). "Open problems in geometry of curves and surfaces" (PDF).

gokovagt.org (Global: low place; English: low place)

Guilfoyle, B.; Klingenberg, W. (2024). "Proof of the Toponogov Conjecture on complete surfaces". J. Gökova Geom. Topol. GGT. 17: 1–50. arXiv:2002.12787.

harvard.edu (Global: 18^th place; English: 17^th place)

ui.adsabs.harvard.edu

Ivanov, V. V. (2002). "The Analytic Carathéodory Conjecture". Sib. Math. J. 43 (2): 251–322. Bibcode:2002SibMJ..43..251I. doi:10.1023/A:1014797105633. ISSN 0037-4474. S2CID 117115329.

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

Bol, G. (1944). "Über Nabelpunkte auf einer Eifläche". Math. Z. 49: 389–410. doi:10.1007/bf01174209. S2CID 120816230.
Guilfoyle, B.; Klingenberg, W. (2019). "Higher codimensional mean curvature flow of compact spacelike submanifolds". Trans. Amer. Math. Soc. 372 (9): 6263–6281. arXiv:1812.00710. doi:10.1090/tran/7766. S2CID 119253397.
Guilfoyle, B.; Klingenberg, W. (2020). "Fredholm-regularity of holomorphic discs in plane bundles over compact surfaces". Ann. Fac. Sci. Toulouse Math. Série 6. 29 (3): 565–576. arXiv:1812.00707. doi:10.5802/afst.1639. S2CID 119659239.
Guilfoyle, B. (2020). "On Isolated Umbilic Points". Comm. Anal. Geom. 28 (8): 2005–2018. arXiv:1812.03562. doi:10.4310/CAG.2020.v28.n8.a8. S2CID 119158738.
Hamburger, H. (1924). "Über Kurvennetze mit isolierten Singularitäten auf geschossenen Flächen". Math. Z. 19: 50–66. doi:10.1007/bf01181063. S2CID 121237690.
Titus, C. J. (1973). "A proof of a conjecture of Loewner and of the conjecture of Carathéodory on umbilic points". Acta Math. 131 (1–2): 43–77. doi:10.1007/BF02392036. S2CID 119377800.
Ivanov, V. V. (2002). "The Analytic Carathéodory Conjecture". Sib. Math. J. 43 (2): 251–322. Bibcode:2002SibMJ..43..251I. doi:10.1023/A:1014797105633. ISSN 0037-4474. S2CID 117115329.
Guilfoyle, B.; Klingenberg, W. (2023). "Roots of polynomials and umbilics of surfaces". Results in Math. 78 (6): 229–247. arXiv:2204.13163. doi:10.1007/s00025-023-02003-4. S2CID 248426964.
Guilfoyle, B.; Klingenberg, W. (2005). "An indefinite Kähler metric on the space of oriented lines". J. London Math. Soc. 72 (2): 497–509. arXiv:math/0407490. doi:10.1112/S0024610705006605. S2CID 14978450.
Guilfoyle, B.; Klingenberg, W. (2004). "Generalised surfaces in $R^{3}$ ". Math. Proc. R. Ir. Acad. 104A (2): 199–209. doi:10.1353/mpr.2004.0013. S2CID 118128548.
Ghomi, M.; Howard, R. (2012). "Normal curvatures of asymptotically constant graphs and Carathéodory's conjecture". Proc. Amer. Math. Soc. 140 (12): 4323–4335. arXiv:1101.3031. doi:10.1090/S0002-9939-2012-11420-0. S2CID 12148752.

uni-goettingen.de (Global: 2,594^th place; English: 2,546^th place)

gdz.sub.uni-goettingen.de

Bol, G. (1944). "Über Nabelpunkte auf einer Eifläche". Math. Z. 49: 389–410. doi:10.1007/bf01174209. S2CID 120816230.

worldcat.org (Global: 5^th place; English: 5^th place)

search.worldcat.org

Sotomayor, J.; Mello, L. F. (1999). "A note on some developments on Carathéodory conjecture on umbilic points". Exposition Math. 17 (1): 49–58. ISSN 0723-0869.
Gutierrez, C.; Sotomayor, J. (1998). "Lines of curvature, umbilic points and Carathéodory conjecture". Resen. Inst. Mat. Estat. Univ. São Paulo. 3 (3): 291–322. ISSN 0104-3854.
Ivanov, V. V. (2002). "The Analytic Carathéodory Conjecture". Sib. Math. J. 43 (2): 251–322. Bibcode:2002SibMJ..43..251I. doi:10.1023/A:1014797105633. ISSN 0037-4474. S2CID 117115329.

Carathéodory conjecture (English Wikipedia)

ams.org (Global: 451st place; English: 277th place)

arxiv.org (Global: 69th place; English: 59th place)

doi.org (Global: 2nd place; English: 2nd place)

gatech.edu (Global: 4,448th place; English: 2,923rd place)