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
DOI:
https://doi.org/10.1090/S0002-9939-1989-0960643-9
MathSciNet review:
960643
Full-text PDF
Abstract | References | Similar Articles | 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
.
- [1] 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)
- [3] S. I. Goldberg, Curvature and homology, Academic Press, New York, 1962. MR 0139098 (25:2537)
- [4] A. M. da Silverira, Stability of complete noncompact surfaces with constant mean curvature, Math. Ann. 277 (1987), 629-638. MR 901709 (88h:53053)
- [5]
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)
- [6] S. Smale, On the Morse index theorem, J. Math. Mech. 14 (1965), 1049-1056. MR 0182027 (31:6251)
- [7] R. L. Bryant, Surfaces of mean curvature one in hyperbolic space (preprint). MR 955072
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53A10, 53C42
Retrieve articles in all journals with MSC: 53A10, 53C42
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1989-0960643-9
Keywords:
Strongly stable,
curvature estimate,
surfaces of constant mean curvature
Article copyright:
© Copyright 1989
American Mathematical Society