Ancient finite entropy flows by powers of curvature in ${\mathbb{R}}^2$

Abstract

We show the existence of non-homothetic ancient flows by powers of curvature embedded in ${\mathbb{R}}^2$ whose entropy is finite. We determine the Morse indices and kernels of the linearized operator of shrinkers to the flows and construct ancient flows by using unstable eigenfunctions of the linearized operator.

Minor changes in some paragraphs. We add several new references in this version