Geodesic boundary of constant mean curvature surfaces in $\mathbb{H}^2\times \mathbb{R}$

TL;DR

This paper generalizes existing results on the geodesic boundary of minimal surfaces in hyperbolic space to include constant mean curvature surfaces with mean curvature between 0 and 1/2.

Contribution

It extends the understanding of the geodesic boundary properties from minimal surfaces to a broader class of constant mean curvature surfaces in hyperbolic space.

Findings

Generalized results for the geodesic boundary of constant mean curvature surfaces

Established properties for surfaces with mean curvature 0 to 1/2

Enhanced the theoretical framework for surfaces in hyperbolic space

Abstract

Some results about the geodesic boundary of minimal surfaces in $\mathbb{H}^2\times \mathbb{R}$ are generalized for surfaces of constant mean curvature surfaces $H$, with $0\le H\le 1/2$.