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

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 ${\mathbb{Q}}_{+}^3$.