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

DOI:
https://doi.org/10.1090/S0002-9939-1995-1286001-0

MathSciNet review:
1286001

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Abstract | References | Similar Articles | Additional Information

Abstract: It has been long conjectured that the two spherical caps are then only discs in the Euclidean three-space 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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Additional Information

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