Stable constant mean curvature hypersurfaces
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- by Maria Fernanda Elbert, Barbara Nelli and Harold Rosenberg PDF
- Proc. Amer. Math. Soc. 135 (2007), 3359-3366 Request permission
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 $|H|$ is large enough. In particular, we prove that there are no complete strongly stable $H$-hypersurfaces in $\mathbb {R}^{n+1}$ without boundary, $H\not =0.$References
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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
- MR Author ID: 150570
- Email: rosen@math.jussieu.fr
- 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
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 3359-3366
- MSC (2000): Primary 53C42
- DOI: https://doi.org/10.1090/S0002-9939-07-08825-9
- MathSciNet review: 2322768