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2003 Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature. II
Wayne Rossman, Masaaki Umehara, Kotaro Yamada
Tohoku Math. J. (2) 55(3): 375-395 (2003). DOI: 10.2748/tmj/1113247480

Abstract

In this work, complete constant mean curvature $1$ (\cmcone{}) surfaces in hyperbolic $3$-space with total absolute curvature at most $4\pi$ are classified. This classification suggests that the Cohn-Vossen inequality can be sharpened for surfaces with odd numbers of ends, and a proof of this is given.

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Wayne Rossman. Masaaki Umehara. Kotaro Yamada. "Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature. II." Tohoku Math. J. (2) 55 (3) 375 - 395, 2003. https://doi.org/10.2748/tmj/1113247480

Information

Published: 2003
First available in Project Euclid: 11 April 2005

zbMATH: 1058.53008
MathSciNet: MR1993862
Digital Object Identifier: 10.2748/tmj/1113247480

Subjects:
Primary: 53A10

Rights: Copyright © 2003 Tohoku University

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