Some characterization, uniqueness and existence results for Euclidean graphs of constant mean curvature with planar boundary
Jaime Ripoll · Pacific Journal of Mathematics · 2001
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. 0. Introduction. In this paper we shall obtain some characterization, uniqueness and existence theorems to the Dirichlet’s problem for the constant mean curvature (cmc) equation with vanishing boundary data