ON A CLASSIFICATION THEOREM FOR SELF-SHRINKERS

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