## Tsukuba Journal of Mathematics

### A duality on $CMC$-1 surfaces in hyperbolic space,and a hyperbolic analogue of the Osserman Inequality

#### Abstract

We will show the existence of a duality on $CMC$-1 surfaces in hyperbolic 3-space, and we will show an analogue of the Osserman Inequality in terms of dual surfaces. Moreover, we will show that equality holds (in this analogue) if and only if all the ends of the surface are regular and embedded.

#### Article information

Source
Tsukuba J. Math., Volume 21, Number 1 (1997), 229-237.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496163174

Digital Object Identifier
doi:10.21099/tkbjm/1496163174

Mathematical Reviews number (MathSciNet)
MR1467234

Zentralblatt MATH identifier
1027.53010

#### Citation

Umehara, Masaaki; Yamada, Kotaro. A duality on $CMC$-1 surfaces in hyperbolic space,and a hyperbolic analogue of the Osserman Inequality. Tsukuba J. Math. 21 (1997), no. 1, 229--237. doi:10.21099/tkbjm/1496163174. https://projecteuclid.org/euclid.tkbjm/1496163174