AN ESTIMATE OF THE PINCHING CONSTANT OF MINIMAL HYPERSURFACES WITH CONSTANT SCALAR CURVATURE IN THE UNIT-SPHERE

Let M(n) (n > 3) be a closed minimal hypersurface with constant scalar curvature in the unit sphere S(n+1)(1) and S the square of the length of its second fundamental form. In this paper we prove that S > n imp lies estimates of the form S > n + cn - d with c greater-than-or-equal -to 1/4. For example, for n > 17 and S > n we prove S > n + 1/4n which is sharper than a recent result of the authors [5]