Stability index jump for cmc hypersurfaces of spheres

Details Stability index jump for cmc hypersurfaces of spheres Stability index jump for cmc hypersurfaces of spheres

2012-02-09

arxiv.org/abs/1202.2050v1

Mathematics

Differential Geometry

4 pages

Scientific paper

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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