Constant mean curvature surfaces in ${\mathbb{H}}^2\times \mathbb{R}$ with boundary in two parallel planes

Abstract

Given $H\in [0,\infty ),$ some sufficient conditions for existence of CMC $H$ graphs with boundary in two parallel planes of ${\mathbb{H}}^2\times \mathbb{R}$ are presented. Height estimates for outwards-oriented CMC surfaces (horo)cyllindrically bounded are also exhibited.

References in corpus (1)

• Non existence of constant mean curvature graphs on circular annuli of ${\mathbb{H}}^2$

Cited by in corpus (2)

• Constant mean curvature graphs in ${\mathbb{H}}^3$ defined in exterior domains
• Geodesic boundary of constant mean curvature surfaces in ${\mathbb{H}}^2\times \mathbb{R}$