Siberian Mathematical Journal

, Volume 43, Issue 2, pp 251–322

The Analytic Caratheodory Conjecture

  • V. V. Ivanov

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.

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • V. V. Ivanov
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirsk