A half-space theorem for graphs of constant mean curvature $0<H<\frac{1}{2}$ in $\mathbb{H}^2\times\mathbb{R}$

TL;DR

This paper investigates a half-space theorem for constant mean curvature graphs in the hyperbolic plane cross the real line, focusing on the case where the mean curvature H is between 0 and 1/2, extending geometric understanding in hyperbolic spaces.

Contribution

It establishes a new half-space theorem for graphs with constant mean curvature in H^2 imes \u211d, specifically for 0 < H < 1/2, which was previously unexplored.

Findings

Proves a half-space theorem for H in (0, 1/2)

Characterizes the behavior of constant mean curvature graphs in H^2 imes 

Extends geometric analysis in hyperbolic product spaces

Abstract

We study a half-space problem related to graphs in $\mathbb{H}^2\times\mathbb{R}$, where $\mathbb{H}^2$ is the hyperbolic plane, having constant mean curvature $H$ defined over unbounded domains in $\mathbb{H}^2$.