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Stability of surfaces with constant mean curvature
Author:
Hai Zhong Li
Journal:
Proc. Amer. Math. Soc. 105 (1989), 992-997
MSC:
Primary 53A10; Secondary 53C42
MathSciNet review:
960643
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Additional Information
Abstract: We estimate the Gaussian curvature of a conformal metric on a surface of constant mean curvature in space form  . By use of the estimates, we study stability of surfaces with constant mean curvature in  .
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- J. L. Barbosa and M. do Carmo, Stability of minimal surfaces and eigenvalues of the Laplacian, Math. Z. 173 (1980), 13-28. MR 584346 (81h:53007)
- [2]
- K. Nomizu and B. Smyth, A formula of Simon's type and hypersurfaces with constant mean curvature, J. Diff. Geom. 3 (1969), 367-377. MR 0266109 (42:1018)
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- S. I. Goldberg, Curvature and homology, Academic Press, New York, 1962. MR 0139098 (25:2537)
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- A. M. da Silverira, Stability of complete noncompact surfaces with constant mean curvature, Math. Ann. 277 (1987), 629-638. MR 901709 (88h:53053)
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- J. L. Barbosa and M. do Carmo, On the size of minimal surface in
 , Amer. J. Math. 98 (2) (1976), 515-528. MR 0413172 (54:1292)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1989-0960643-9
PII:
S 0002-9939(1989)0960643-9
Keywords:
Strongly stable,
curvature estimate,
surfaces of constant mean curvature
Article copyright:
© Copyright 1989 American Mathematical Society
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