Rearrangements and radial graphs of constant mean curvature in hyperbolic space

TL;DR

This paper studies smooth hypersurfaces with constant mean curvature in hyperbolic space, using variational methods and rearrangement techniques to analyze their properties as radial graphs over the upper hemisphere.

Contribution

It introduces a variational approach combined with rearrangement techniques to analyze constant mean curvature hypersurfaces in hyperbolic space as radial graphs.

Findings

Existence of smooth constant mean curvature hypersurfaces as radial graphs

Application of rearrangement techniques in hyperbolic geometry

New variational methods for studying hypersurfaces in hyperbolic space

Abstract

We investigate the problem of finding smooth hypersurfaces of constant mean curvature in hyperbolic space, which can be represented as radial graphs over a subdomain of the upper hemisphere. Our approach is variational and our main results are proved via rearrangement techniques.