Siberian Mathematical Journal

, Volume 43, Issue 2, pp 251-322

First online:

The Analytic Caratheodory Conjecture

  • V. V. IvanovAffiliated withSobolev Institute of Mathematics

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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.