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arXiv · 1202.2050

Stability index jump for cmc hypersurfaces of spheres

Oscar M. Perdomo·Aldir Brasil
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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.

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Oscar M. Perdomo, Aldir Brasil. 2012-02-09. Stability index jump for cmc hypersurfaces of spheres. https://arxiv.org/abs/1202.2050

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