Some Characterization, Uniqueness and Existence Results for Euclidean Graphs of Constant Mean Curvature with Planar Boundary
نویسندگان
چکیده
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.
منابع مشابه
An Existence Theorem of Constant Mean Curvature Graphs in Euclidean Space*
We prove the following result of existence of graphs with constant mean curvature in Euclidean space: given a convex bounded planar domain of area að Þ and a real number H such that að ÞH < =2, there exists a graph on with constant mean curvature H and whose boundary is @ . 2000 Mathematics Subject Classification. 53A10, 53C42.
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