# The Analytic Caratheodory Conjecture

@article{Ivanov2002TheAC,
title={The Analytic Caratheodory Conjecture},
journal={Siberian Mathematical Journal},
year={2002},
volume={43},
pages={251-322}
}
• V. V. Ivanov
• Published 1 March 2002
• Mathematics
• Siberian Mathematical Journal
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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