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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stable constant mean curvature hypersurfaces


Authors: Maria Fernanda Elbert, Barbara Nelli and Harold Rosenberg
Journal: Proc. Amer. Math. Soc. 135 (2007), 3359-3366
MSC (2000): Primary 53C42
Published electronically: June 19, 2007
MathSciNet review: 2322768
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Abstract: Let $ {\mathcal N}^{n+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 $ \vert H\vert$ is large enough. In particular, we prove that there are no complete strongly stable $ H$-hypersurfaces in $ \mathbb{R}^{n+1}$ without boundary, $ H\not=0.$


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Additional Information

Maria Fernanda Elbert
Affiliation: Instituto de Matematica, Universidade Federal do Rio de Janeiro, Rio de Janiero, Brazil
Email: fernanda@im.ufrj.br

Barbara Nelli
Affiliation: Dipartimento di Matematica Pura e Applicata, Universitá di L’Aquila, Via Vetoio, 67010 Coppito L’Aquila, Italy
Email: nelli@univaq.it

Harold Rosenberg
Affiliation: Institut de Mathématiques, Université Paris VII, 2 place Jussieu, 75251 Paris, France
Email: rosen@math.jussieu.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08825-9
PII: S 0002-9939(07)08825-9
Received by editor(s): January 24, 2006
Received by editor(s) in revised form: May 17, 2006
Published electronically: June 19, 2007
Additional Notes: The first author was partially supported by CNPq and Faperj.
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2007 American Mathematical Society