, Volume 99, Issue 5, pp 493-500
Date: 16 Nov 2012

Stability index jump for constant mean curvature hypersurfaces of spheres

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.

To Myriam Santamaria