An a priori estimate for the Gauss curvature of nonparametric surfaces of constant mean curvature

Spruck, Joel

doi:10.1090/S0002-9939-1972-0307056-8

An a priori estimate for the Gauss curvature of nonparametric surfaces of constant mean curvature
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Proc. Amer. Math. Soc. 36 (1972), 217-223 Request permission

Abstract:

We consider surfaces of constant mean curvature in three-dimensional Euclidean space which have a nonparametric representation over a disc. It is shown that if the surface has a horizontal tangent plane at the origin of the disc, then the Gauss curvature of the surface at the origin satisfies an a priori bound. The existence of a bound is established by identifying and proving the existence of an extremal surface.

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Sur la surface de revolution dont la courbure moyenne est constante

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