Stable constant mean curvature hypersurfaces

Elbert, Maria; Nelli, Barbara; Rosenberg, Harold

doi:10.1090/S0002-9939-07-08825-9

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, $H\not =0.$

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