On the rigidity of self-shrinkers of the r-mean curvature flow

Abstract

In this paper, we consider self-similar solutions of the [Formula: see text]-mean curvature flow into the [Formula: see text]-dimensional Euclidean space. By employing some general maximum principles as the main tool, we characterize some self-similar solutions of the [Formula: see text]-mean curvature flow under some suitable geometric constraints.