Generic non-uniqueness of complete $H$-surfaces embedded in $\mathbb{H}^3$

Cagri Haciyusufoglu

Generic non-uniqueness of complete $H$-surfaces embedded in $\mathbb{H}^3$

Differential Geometry 2016-02-08 v1

Authors: Cagri Haciyusufoglu

Abstract

We prove that, given $|H|<1$ , a generic simple closed curve embedded in the asymptotic boundary of $\mathbb{H}^3$ (with respect to the supremum metric) bounds more than one complete surface embedded in $\mathbb{H}^3$ which has constant mean curvature $H$ . We remark that this is not true for the space of simple closed $\text{C}^1$ -curves.

Keywords

surfaces and embeddings surfaces with constant mean curvature hypersurfaces

Cite

@article{arxiv.1602.02006,
  title  = {Generic non-uniqueness of complete $H$-surfaces embedded in $\mathbb{H}^3$},
  author = {Cagri Haciyusufoglu},
  journal= {arXiv preprint arXiv:1602.02006},
  year   = {2016}
}

Comments

9 pages, 2 figures

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