Existence of constant mean curvature graphs in hyperbolic space

• DOI: 10.1007/s005260050122
• Publication Date: 2002-08-25T05:09:23Z
• Authors: Rafael López; Sebastián Montiel
• Keywords: 0101 mathematics; 01 natural sciences

We give an existence result for constant mean curvature graphs in hyperbolic space H n+1 . Let be a compact domain of a horosphere in H n+1 whose boundary @ is mean convex, that is, its mean curvature H@ (as a submanifold of the horosphere) is positive with respect to the inner orientation. If H is a number such that H@ < H < 1, then there exists a graph over with constant mean curvature H and boundary @. Umbilical examples, when @ is a sphere, show that our hypothesis on H is the best possible.