A Gap Theorem for Self-shrinkers of the Mean Curvature Flow in Arbitrary Codimension

preprint2012arXivOpen access

Abstract

In this paper, we prove a classification theorem for self-shrinkers of the mean curvature flow with ∣A∣2≤1|A|^2\le 1 in arbitrary codimension. In particular, this implies a gap theorem for self-shrinkers in arbitrary codimension.

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