Abstract

ALIAS, Luis J.. On the stability index of minimal and constant mean curvature hypersurfaces in spheres. Rev. Unión Mat. Argent. [online]. 2006, vol.47, n.2, pp.39-61. ISSN 0041-6932.

The study of minimal and, more generally, constant mean curvature hypersurfaces in Riemannian space forms is a classical topic in differential geometry. As is well known, minimal hypersurfaces are critical points of the variational problem of minimizing area. Similarly, hypersurfaces with constant mean curvature are also solutions to that variational problem, when restricted to volume-preserving variations. In this paper we review about the stability index of both minimal and constant mean curvature hypersurfaces in Euclidean spheres, including some recent progress by the author, jointly with some of his collaborators. One of our main objectives on writing this paper has been to make it comprehensible for a wide audience, trying to be as self-contained as possible.

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