Stability index jump for cmc hypersurfaces of spheres
Differential Geometry
2012-02-10 v1
Abstract
It is known that the totally umbilical hypersurfaces in the (n+1)-dimensional spheres are characterized as the only hypersurfaces with weak stability index 0. That is, a compact hypersurface with constant mean curvature, cmc, in S^{n+1}, different from an Euclidean sphere, must have stability index greater than or equal to 1. In this paper we prove that the weak stability index of any non-totally umbilical compact hypersurface M\subset S^{n+1} with cmc cannot take the values 1,2,3... n.
Keywords
Cite
@article{arxiv.1202.2050,
title = {Stability index jump for cmc hypersurfaces of spheres},
author = {Oscar M. Perdomo and Aldir Brasil},
journal= {arXiv preprint arXiv:1202.2050},
year = {2012}
}
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4 pages