Classification and rigidity of self-shrinkers in the Mean curvature flow

Abstract

In this paper, we first use the method of Colding and Minicozzi [5] to show that K. Smoczyk's classification theorem [16] for complete self-shrinkers in higher codimension also holds under a weaker condition. Then as an application, we give some rigidity results for self-shrinkers in arbitrary codimension.

26 pages, to appear in Journal of the Mathematical Society of Japan

References in corpus (3)

• Evolution of curves and surfaces by mean curvature
• Generic mean curvature flow I; generic singularities
• $\mathcal{F}$-stability for self-shrinking solutions to mean curvature flow

Cited by in corpus (4)

• The Clifford torus as a self-shrinker for the Lagrangian mean curvature flow
• Complete $\lambda$-hypersurfaces of weighted volume-preserving mean curvature flow
• Complete self-shrinkers of the mean curvature flow
• A gap theorem of self-shrinkers