Translator Disclaimer
March 2004 Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature. I
Wayne Rossman, Masaaki Umehara, Kotaro Yamada
Hiroshima Math. J. 34(1): 21-56 (March 2004). DOI: 10.32917/hmj/1150998070

Abstract

A complete surface of constant mean curvature 1 (CMC-1) in hyperbolic 3- space with constant curvature $-1$ has two natural notions of ‘‘total curvature’’—one is the total absolute curvature which is the integral over the surface of the absolute value of the Gaussian curvature, and the other is the dual total absolute curvature which is the total absolute curvature of the dual CMC-1 surface. In this paper, we completely classify CMC-1 surfaces with dual total absolute curvature at most $4\pi$. Moreover, we give new examples and partially classify CMC-1 surfaces with dual total absolute curvature at most $8\pi$.

Citation

Download Citation

Wayne Rossman. Masaaki Umehara. Kotaro Yamada. "Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature. I." Hiroshima Math. J. 34 (1) 21 - 56, March 2004. https://doi.org/10.32917/hmj/1150998070

Information

Published: March 2004
First available in Project Euclid: 22 June 2006

zbMATH: 1088.53004
MathSciNet: MR2046452
Digital Object Identifier: 10.32917/hmj/1150998070

Subjects:
Primary: 53A10
Secondary: 53A35

Rights: Copyright © 2004 Hiroshima University, Mathematics Program

JOURNAL ARTICLE
36 PAGES


SHARE
Vol.34 • No. 1 • March 2004
Back to Top