Global properties of constant mean curvature surfaces in ℍ² × ℝ

Barbara Nelli and Harold Rosenberg

Vol. 226 (2006), No. 1, 137–152

DOI: 10.2140/pjm.2006.226.137

Abstract

We discuss some aspects of the global behavior of surfaces in ℍ² × ℝ with constant mean curvature H (known as H-surfaces). We prove a maximum principle at infinity for complete properly embedded H-surfaces with H > 1∕, and show that the genus of a compact stable H-surface with H > 1∕ is at most three.

Keywords

mean curvature, stability, maximum principle at infinity

Mathematical Subject Classification 2000

Primary: 53A10, 35J60

Milestones

Received: 19 August 2004

Revised: 4 February 2005

Accepted: 8 April 2005

Published: 1 July 2006