English

Height estimates for constant mean curvature graphs in $\mathrm{Nil}_3$ and $\widetilde{PSL}_2(\mathbb{R})$

Differential Geometry 2019-03-19 v3

Abstract

In this paper we obtain height estimates for compact, constant mean curvature vertical graphs in the homogeneous spaces Nil3\mathrm{Nil}_3 and PSL~2(R)\widetilde{PSL}_2(\mathbb{R}). As a straightforward consequence, we announce a structure-type result for proper graphs defined on relatively compact domains.

Keywords

Cite

@article{arxiv.1803.06688,
  title  = {Height estimates for constant mean curvature graphs in $\mathrm{Nil}_3$ and $\widetilde{PSL}_2(\mathbb{R})$},
  author = {Antonio Bueno},
  journal= {arXiv preprint arXiv:1803.06688},
  year   = {2019}
}