Stable Constant Mean Curvature Hypersurfaces

@inproceedings{ELBERT2007StableCM,
  title={Stable Constant Mean Curvature Hypersurfaces},
  author={MARIA FERNANDA ELBERT and B. Nelli and Richard A. Wentworth},
  year={2007}
}
Let Nn+1 be a Riemannian manifold with sectional curvatures uniformly bounded from below. When n = 3, 4, we prove that there are no complete (strongly) stable H-hypersurfaces, without boundary, provided |H| is large enough. In particular, we prove that there are no complete strongly stable H-hypersurfaces in Rn+1 without boundary, H = 0. 

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 10 references

Constant Mean Curvature Surfaces in Homogeneously Regular 3-Manifold, Preprint (2005) http://www.math.jussieu.fr/∼ rosen

H. Rosenberg
2005

On Complete Hypersurfaces with Constant Mean Curvature and Finite Lp-norm Curvature in Rn+1

Y. B. Shen, X. H. Zhu
Acta Math. Sinica, English series 21, • 2005

Eigenvalue and “Twisted

J. L. Barbosa, P. Bérard
Eigenvalue Problems, Applications to CMC Surfaces, J. Math. Pures Appl. 79, • 2000

Rigidity of Stable Minimal Hypersurfaces

Y. Shen, S. Zhu
Math. Annalen • 1997

Yau: Lectures on Differential Geometry

S.T.R. Schoen
1994

On Complete Minimal Surfaces with finite Morse Index in three Manifolds

D. Fischer-Colbrie
Inv. Math • 1985

Stability of Hypersurfaces with Constant Mean Curvature, Math. Zeit

J. L. Barbosa, M. do Carmo
1984

Peng: Stable Complete Minimal Hypersurfaces

C.K.M. do Carmo
Proceedings of the 1980 Beijing Symposium on Diff. Geom. and Diff. Eq., • 1982

Similar Papers

Loading similar papers…