A lower bound for the norm of the second fundamental form of minimal hypersurfaces of Sn+1

Abstract

The aim of this paper is to give an estimate for the squared norm S of the second fundamental form A of a compact minimal hypersurface Mn⊂Sn+1 in terms of the gap n−λ1 , where λ1 stands for the first eigenvalue of the Laplacian of M. More precisely we will show that there exists a constant k≥nn−1 such that S≥kn−1n(n−λ1).