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VOL. 34 | 2002 Constant Mean Curvature 1 Surfaces with Low Total Curvature in Hyperbolic 3-Space
Wayne Rossman, Masaaki Umehara, Kotaro Yamada

Editor(s) Kenji Fukaya, Seiki Nishikawa, Joel Spruck

Abstract

Surfaces of constant mean curvature one in hyperbolic 3-space have quite similar properties to minimal surfaces in Euclidean 3-space. We shall list the possibilities of constant mean curvature one surfaces in hyperbolic 3-space with low total absolute curvature, or low dual total absolute curvature, and compare them with the known classification of minimal surfaces with low total curvature. Complete proofs of the new results will be published in two forthcoming papers (listed in the bibliography).

Information

Published: 1 January 2002
First available in Project Euclid: 31 December 2018

zbMATH: 1035.53018
MathSciNet: MR1925744

Digital Object Identifier: 10.2969/aspm/03410245

Subjects:
Primary: 53A10
Secondary: 53A35, 53A42

Rights: Copyright © 2002 Mathematical Society of Japan

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