Siberian Mathematical Journal

, Volume 43, Issue 2, pp 251–322

The Analytic Caratheodory Conjecture


  • V. V. Ivanov
    • Sobolev Institute of Mathematics

DOI: 10.1023/A:1014797105633

Cite this article as:
Ivanov, V.V. Siberian Mathematical Journal (2002) 43: 251. doi:10.1023/A:1014797105633


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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© Plenum Publishing Corporation 2002