Non-uniqueness of self-similar shrinking curves for an anisotropic curvature flow

Abstract

In this paper, we consider self-similar solutions for an anisotropic curvature flow equation in the plane. For some (nonsymmetric) interfacial energy, we show that there exists a self-similar curve which is not a local minimizer of the entropy under the area constraint. As its result, we obtain non-uniqueness of self-similar solutions for the anisotropic flow.