Soliton solutions for the mean curvature flow

Abstract

We consider soliton solutions of the mean curvature flow, i.e., solutions which move under the mean curvature flow by a group of isometries of the ambient manifold. Several examples of solitons on manifolds are discussed. Moreover we present a local existence result for rotating solitons. We also prove global existence and stability for perturbed initial data close to a local soliton.