Cylindrically bounded constant mean curvature surfaces in $\mathbb{H}^2\times\mathbb{R}$

Laurent Mazet

Cylindrically bounded constant mean curvature surfaces in $\mathbb{H}^2\times\mathbb{R}$

Differential Geometry 2013-11-12 v3

Authors: Laurent Mazet

Abstract

In this paper we prove that a properly embedded constant mean curvature surface in $\mathbb{H}^2\times\mathbb{R}$ which has finite topology and stays at a finite distance from a vertical geodesic line is invariant by rotation around a vertical geodesic line.

Keywords

constant mean curvature surfaces $\mathbb{H}^2\times\mathbb{R}$ finite topology proper embedding vertical geodesic line rotational invariance

Cite

@article{arxiv.1203.2746,
  title  = {Cylindrically bounded constant mean curvature surfaces in $\mathbb{H}^2\times\mathbb{R}$},
  author = {Laurent Mazet},
  journal= {arXiv preprint arXiv:1203.2746},
  year   = {2013}
}

Comments

34 pages, 5 figures

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