On Chernʼs problem for rigidity of minimal hypersurfaces in the spheres

For a compact minimal hypersurface M in Sn+1 with the squared length of the second fundamental form S we confirm that there exists a positive constant δ(n) depending only on n, such that if n⩽S⩽n+δ(n), then S≡n, i.e., M is a Clifford minimal hypersurface, in particular, when n⩾6, the pinching constant .