An existence theorem of constant mean curvature graphs in Euclidean space Research partially supported by DGICYT grant number PB97-0785.

Abstract

We prove the following result of existence of graphs with constant mean curvature in Euclidean space: given a convex bounded planar domain \Omega of area a(\Omega) and a real number H such that a(\Omega)H^2<\pi/2, there exists a graph on \Omega with constant mean curvature H and whose boundary is \partial\Omega.