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Proceedings of the American Mathematical Society

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

 

 

Constant mean curvature discs with bounded area


Authors: Rafael López and Sebastián Montiel
Journal: Proc. Amer. Math. Soc. 123 (1995), 1555-1558
MSC: Primary 53A10
MathSciNet review: 1286001
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Abstract: It has been long conjectured that the two spherical caps are then only discs in the Euclidean three-space $ {\mathbb{R}^3}$ with non-zero constant mean curvature spanning a round circle. In this work, we prove that it is true when the area of such a disc is less than or equal to that of the big spherical cap.


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DOI: https://doi.org/10.1090/S0002-9939-1995-1286001-0
Keywords: Constant mean curvature, disc, isoperimetric inequality
Article copyright: © Copyright 1995 American Mathematical Society