Translator Disclaimer
2001 Mean curvature {$1$} surfaces of Costa type in hyperbolic three-space
Celso J. Costa, Vicente F. Sousa Neto
Tohoku Math. J. (2) 53(4): 617-628 (2001). DOI: 10.2748/tmj/1113247804

Abstract

In this paper we prove the existence of families of complete mean curvature one surfaces in the hyperbolic three-space. We show that for each Costa-Hoffman-Meeks embedded minimal surface of positive genus in Euclidean three-space, we can produce, by cousin correspondence, a family of complete mean curvature one surfaces in the hyperbolic three-space. These surfaces have positive genus, three ends and the same group of symmetry of the original minimal surfaces. Furthermore, two of the ends approach the same point in the ideal boundary of hyperbolic three-space and the third end is asymptotic to a horosphere. The method we use to produce these results were developed in a recent paper by W. Rossman, M. Umehara and K. Yamada.

Citation

Download Citation

Celso J. Costa. Vicente F. Sousa Neto. "Mean curvature {$1$} surfaces of Costa type in hyperbolic three-space." Tohoku Math. J. (2) 53 (4) 617 - 628, 2001. https://doi.org/10.2748/tmj/1113247804

Information

Published: 2001
First available in Project Euclid: 11 April 2005

zbMATH: 1014.53007
MathSciNet: MR1862222
Digital Object Identifier: 10.2748/tmj/1113247804

Subjects:
Primary: 53A10

Rights: Copyright © 2001 Tohoku University

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.53 • No. 4 • 2001
Back to Top