A height estimate for H -surfaces and existence of H -graphs
Copyright policy )A height estimate for H -surfaces and existence of H -graphs
Let Ω be a bounded planar domain which is convex (although not necessarily strictly convex) with area A . We prove that, for each real number H satisfying AH 2 < ρ 2 π, with ρ = (√5 - 1)/2, there exists a graph on Ω with constant mean curvature H and boundary ∂Ω. This existence theorem is deduced as a consequence of an L ∞ estimate for compact constant mean curvature surfaces with planar boundary, in terms of the L 1 norm of a component of its Gauss map, which will be obtained in this paper.
height estimate, Gauss map, constant mean curvature, Minimal surfaces in differential geometry, surfaces with prescribed mean curvature, Dirichlet problem
height estimate, Gauss map, constant mean curvature, Minimal surfaces in differential geometry, surfaces with prescribed mean curvature, Dirichlet problem
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