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.

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

References in corpus (5)

• Uniqueness of compact ancient solutions to three-dimensional Ricci flow
• Ancient gradient flows of elliptic functionals and Morse index
• Ancient solutions to the Ricci flow in dimension 3
• Unique Asymptotics of Compact Ancient Solutions to three-dimensional Ricci flow
• Mean curvature flow with generic initial data

Cited by in corpus (2)

• Translating surfaces under flows by sub-affine-critical powers of Gauss curvature
• Classification of ancient flows by sub-affine-critical powers of curvature in ${\mathbb{R}}^2$