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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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


Author: Joel Spruck
Journal: Proc. Amer. Math. Soc. 36 (1972), 217-223
MSC: Primary 53A10
DOI: https://doi.org/10.1090/S0002-9939-1972-0307056-8
MathSciNet review: 0307056
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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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DOI: https://doi.org/10.1090/S0002-9939-1972-0307056-8
Keywords: Constant mean curvature, minimal surfaces, Gauss curvature, a priori estimate, Scherk surface, comparison methods, maximum principle
Article copyright: © Copyright 1972 American Mathematical Society