Proceedings of the American Mathematical Society

Author(s): Maria Fernanda Elbert; Barbara Nelli; Harold Rosenberg
Journal: Proc. Amer. Math. Soc. 135 (2007), 3359-3366.
MSC (2000): Primary 53C42
Posted: June 19, 2007
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Abstract: Let ${\mathcal N}^{n+1}$ be a Riemannian manifold with sectional curvatures uniformly bounded from below. When

we prove that there are no complete (strongly) stable

-hypersurfaces, without boundary, provided $\vert H\vert$ is large enough. In particular, we prove that there are no complete strongly stable

-hypersurfaces in $\mathbb{R}^{n+1}$ without boundary, $H\not=0.$

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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

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