Low index minimal hypersurfaces of spheres (Q700528)

Let \(M\) be a compact oriented non-equatorial minimal hypersurface of the \(n\)-dimensional unit sphere. The author proves that, i) the stability index of \(M\) is greater than or equal to \(n+2\), with inequality when \(M\) is a Clifford hypersurface; ii) the difference of the two eigenvalues of the Jacobian operators is equal to \(n-1\), if the norm of the second fundamental form is constant, otherwise it is less than \(n-1\); and (iii) if \(M\) has antipodal symmetry and is not a Clifford hypersurface, then the index is greater than \(n+3\).