Spacelike Graphs of Prescribed Mean Curvature in the Steady State Space

Abstract

Abstract We study the Dirichlet problem of the constant mean curvature equation in the steady state space over a bounded domain of a slice. Under suitable conditions on the convexity of the domain, we prove the existence of a spacelike graph with constant mean curvature H, with - 1 ≤ H < 0 ${-1\leq H<0}$ , and constant boundary values.