On a classification theorem for self-shrinkers

Abstract

We generalize a classification result for self-shrinkers of the mean curvature flow with nonnegative mean curvature, which was obtained by T. Colding and W. Minicozzi, replacing the assumption on polynomial volume growth with a weighted $L^2$ condition on the norm of the second fundamental form. Our approach adopt the viewpoint of weighted manifolds and permits also to recover and to extend some others recent classification and gap results for self-shrinkers.

9 pages. To appear on Proc. Amer. Math. Soc

References in corpus (1)

• Complete self-shrinkers of the mean curvature flow

Cited by in corpus (6)

• Stability properties and topology at infinity of f-minimal hypersurfaces
• Complete self-shrinkers confined into some regions of the space
• Rigidity results and topology at infinity of translating solitons of the mean curvature flow
• Volume growth, entropy and stability for translating solitons
• Rigidity and gap results for low index properly immersed self--shrinkers in ${\mathbb{R}}^{m+1}$
• Rigidity of complete self-shrinkers whose tangent planes omit a nonempty set