A HEIGHT ESTIMATE FOR H-SURFACES AND EXISTENCE OF H-GRAPHS By SEBASTIÁN MONTIEL

نویسنده

SEBASTIÁN MONTIEL

چکیده

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 AH2 < 2 , with = ( p 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 L1 norm of a component of its Gauss map, which will be obtained in this paper.

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