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1996 On a conjecture of Carathéodory: analyticity versus smoothness
Carlos Gutierrez, Francesco Mercuri, Federico Sánchez-Bringas
Experiment. Math. 5(1): 33-37 (1996).

Abstract

We show that, under mild nonflatness conditions, for any $r\ge 3$ and any $C^r$-immersion of a surface into $\R^3$ with an isolated umbilic point there exist an analytic surface with an isolated umbilic of the same index. The connection of this with Carathéodory's Conjecture on umbilics is discussed.

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Carlos Gutierrez. Francesco Mercuri. Federico Sánchez-Bringas. "On a conjecture of Carathéodory: analyticity versus smoothness." Experiment. Math. 5 (1) 33 - 37, 1996.

Information

Published: 1996
First available in Project Euclid: 13 March 2003

zbMATH: 0862.57023
MathSciNet: MR1412952

Subjects:
Primary: 53A05

Rights: Copyright © 1996 A K Peters, Ltd.

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Vol.5 • No. 1 • 1996
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