Some characterization, uniqueness and existence results for Euclidean graphs of constant mean curvature with planar boundary

Jaime Ripoll

Vol. 198 (2001), No. 1, 175–196

DOI: 10.2140/pjm.2001.198.175

Abstract

We establish the existence and uniqueness of solutions to the Dirichlet problem for the cmc surface equation, including the minimal one, for zero boundary data, in certain domains of the plane. We obtain results that characterize the sphere and cmc graphs among compact embedded cmc surfaces with planar boundary satisfying certain geometric conditions. We also find conditions that imply that a compact embedded cmc surface which is a graph near the boundary is indeed a global graph.

Milestones

Received: 19 February 1999

Published: 1 March 2001