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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Stable complete constant mean curvature surfaces in $ {\bf R}\sp{3}$ and $ H\sp{3}$


Author: Hiroshi Mori
Journal: Trans. Amer. Math. Soc. 278 (1983), 671-687
MSC: Primary 58E12; Secondary 49F10, 53C42
MathSciNet review: 701517
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Abstract: We construct some $ 1$-parameter families of complete rotation surfaces with constant mean curvature in the hyperbolic $ 3$-space $ {H^3}$ of constant sectional curvature $ -1$, and show that some of them are stable for the variational problem of area together with oriented volume, and that a complete connected, oriented surface with constant mean curvature in the Euclidean $ 3$-space $ {R^3}$ which is stable for the variational problem is a plane.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0701517-7
PII: S 0002-9947(1983)0701517-7
Keywords: Rotation surfaces, mean curvature, variational problem, stable
Article copyright: © Copyright 1983 American Mathematical Society