Bernstein-type Theorems for constant mean curvature surfaces in the three-dimensional light cone

TL;DR

This paper proves Bernstein-type theorems for entire constant mean curvature graphs in the 3D light cone, showing they are either horospheres or spheres when Gaussian curvature is bounded below.

Contribution

It establishes new Bernstein-type classification results for constant mean curvature surfaces in the light cone under curvature bounds.

Findings

Constant mean curvature graphs are classified as horospheres or spheres.

Theorems hold under the assumption of Gaussian curvature bounded below.

Results extend classical Bernstein theorems to Lorentzian geometry.

Abstract

We establish Bernstein-type theorems for entire constant mean curvature graphs in the three-dimensional light cone $\mathbb{Q}^3_+$ over the horosphere under the assumption that the Gaussian curvature $K$ is bounded below, by showing that such graphs are horospheres or spheres of $\mathbb{Q}^3_+$.