A GLOBAL PINCHING THEOREM FOR COMPACT MINIMAL-SURFACES IN-S3

Abstract

Let M be a compact minimally immersed surface in the unit sphere S3, and let S denote the square of the length of the second fundamental form of M. We prove that if parallel-to S parallel-to 2 less-than-or-equal-to 2 square-root 2-pi, then M is either the equatorial sphere or the Clifford torus.