Constant mean curvature graphs in $\mathbb{H}^3$ defined in exterior domains

Patricia Klaser; Adilson Nunes; Jaime Ripoll

Constant mean curvature graphs in $\mathbb{H}^3$ defined in exterior domains

Differential Geometry 2024-07-16 v2 Analysis of PDEs

Authors: Patricia Klaser , Adilson Nunes , Jaime Ripoll

Abstract

Given $H\in [0,1)$ and given a $C^0$ exterior domain $\Omega$ in a $H-$ hypersphere of $\mathbb{H}^3,$ the existence of hyperbolic Killing graphs of CMC $H$ defined in $\overline{\Omega}$ with boundary $\partial \Omega$ included in the $H-$ hypersphere is obtained.

Keywords

constant mean curvature hyperbolic Killing graphs exterior domains H-hypersphere H^3 existence

Cite

@article{arxiv.2109.07970,
  title  = {Constant mean curvature graphs in $\mathbb{H}^3$ defined in exterior domains},
  author = {Patricia Klaser and Adilson Nunes and Jaime Ripoll},
  journal= {arXiv preprint arXiv:2109.07970},
  year   = {2024}
}

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