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The Analytic Caratheodory Conjecture

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Abstract

The aim of this article is to provide the reader with a real possibility of becoming confident that the index of an isolated umbilic point of an analytic surface is never greater than one. For a surface homeomorphic to a sphere, this means in particular that on the surface there necessarily exist at least two umbilic points as it was conjectured by Caratheodory.

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References

  1. Hamburger H., “Beweis einer Carathéodoryschen Vermütung,” I: Ann. of Math. Ser. 2, 41, 63-86 (1940); II and III: Acta Math., 73, 174-332 (1941).

    Google Scholar 

  2. Bol G.,“Über Nabelpunkte auf einer Eifläche,” Math. Z., 49, 389-410 (1943-1944).

    Google Scholar 

  3. Klotz T., “On G. Bol's proof of Carathéodory's conjecture,” Comm. Pure Appl. Math., 12, No. 2, 277-311 (1959).

    Google Scholar 

  4. Titus C. J., “A proof of a conjecture of Loewner and of the conjecture of Carathéodory on umbilic points,” Acta Math., 131, No. 1-2, 43-77 (1973).

    Google Scholar 

  5. Sotomayor J. and Mello L. F., “A note on some developments on Carathéodory conjecture on umbilic points,” Exposition. Math., 17, No. 1, 49-58 (1999).

    Google Scholar 

  6. Gutierrez C. and Sotomayor J., “Lines of curvature, umbilic points and Carathéodory conjecture,” Resenhas IME-USP, 3, No. 3, 291-322 (1998).

    Google Scholar 

  7. Blaschke W., Differential Geometry and the Geometrical Foundations of the Einstein Relativity Theory. Vol. 1: Elementary Differential Geometry [Russian translation], ONTI NKTP SSSR, Moscow and Leningrad (1935).

    Google Scholar 

  8. Goursat E., A Course of Mathematical Analysis. II: The Theory of Analytic Functions. Differential Equations [Russian translation], ONTI NKTP SSSR, Moscow and Leningrad (1936).

    Google Scholar 

  9. van der Waerden B. L., Algebra [Russian translation], Nauka, Moscow (1979).

    Google Scholar 

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk

    V. V. Ivanov

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  1. V. V. Ivanov
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Ivanov, V.V. The Analytic Caratheodory Conjecture. Siberian Mathematical Journal 43, 251–322 (2002). https://doi.org/10.1023/A:1014797105633

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  • DOI: https://doi.org/10.1023/A:1014797105633

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