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Proceedings of the American Mathematical Society

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

 

 

A characterization of compact surfaces with constant mean curvature


Author: Masaaki Umehara
Journal: Proc. Amer. Math. Soc. 108 (1990), 483-489
MSC: Primary 53C42; Secondary 53A10
DOI: https://doi.org/10.1090/S0002-9939-1990-0987616-2
MathSciNet review: 987616
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Abstract: Surfaces in a $ 3$-space of constant curvature, whose arbitrary sufficiently small open subsets admit a non-trivial isometric deformation preserving the mean curvature function, are called locally $ H$-deformable. It is well known that surfaces with constant mean curvature which are not totally umbilical are all locally $ H$-deformable. Conversely, we shall show in this paper that any compact locally $ H$-deformable surface has constant mean curvature.


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DOI: https://doi.org/10.1090/S0002-9939-1990-0987616-2
Keywords: Surfaces with constant mean curvature, $ H$-deformation
Article copyright: © Copyright 1990 American Mathematical Society