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

Kyeongsu Choi; Liming Sun

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

Differential Geometry 2020-12-21 v2

Authors: Kyeongsu Choi , Liming Sun

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.

Keywords

ancient flows powers of curvature finite entropy shrinkers linearized operator morse index

Cite

@article{arxiv.2011.02639,
  title  = {Ancient finite entropy flows by powers of curvature in $\mathbb{R}^2$},
  author = {Kyeongsu Choi and Liming Sun},
  journal= {arXiv preprint arXiv:2011.02639},
  year   = {2020}
}

Comments

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

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