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

Rodrigo Soares; Patrícia Klaser; Miriam Telichevesky

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

Differential Geometry 2015-12-25 v1

Authors: Rodrigo Soares , Patrícia Klaser , Miriam Telichevesky

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.

Keywords

constant mean curvature surfaces hyperbolic plane height estimates boundary conditions differential geometry

Cite

@article{arxiv.1512.07637,
  title  = {Constant mean curvature surfaces in $\mathbb{H}^2\times\mathbb{R}$ with boundary in two parallel planes},
  author = {Rodrigo Soares and Patrícia Klaser and Miriam Telichevesky},
  journal= {arXiv preprint arXiv:1512.07637},
  year   = {2015}
}

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