Pinching Theorems for Self-shrinkers of Higher Codimensions

Abstract

Abstract. In this paper, we investigate the pinching phenomena of the tracefree second fundamental form of complete self-shrinkers of higher codimension. Firstly, assuming the mean curvature is nonzero everywhere and the selfshrinker is of polynomial volume growth, we prove that if the tracefree second fundamental form Å satisfies ||Å||n < C(n) for a… (More)

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