Title: Index bounds for minimal hypersurfaces of the sphere

Authors: Alessandro Savo

Issue: Volume 59 (2010), Issue 3, 823-838

Abstract: We consider a compact, orientable minimal hypersurfaces of the unit sphere and prove a comparison theorem between the spectrum of the stability operator and that of the Laplacian on $1$-forms. As a corollary, we show that the index is bounded below by a linear function of the first Betti number; in particular, if the first Betti number is large, then the immersion is highly unstable.