Curve shortening flow on Riemann surfaces with possible ambient conic singularities

Biao Ma

Curve shortening flow on Riemann surfaces with possible ambient conic singularities

Differential Geometry 2022-05-09 v3

Authors: Biao Ma

Abstract

In this paper, we study the curve shortening flow (CSF) on Riemann surfaces. We generalize Huisken's comparison function to Riemann surfaces and surfaces with conic singularities. We reprove the Gage-Hamilton-Grayson theorem on surfaces. We also prove that for embedded simple closed curves, CSF can not touch conic singularities with cone angles $\leq \pi$ .

Keywords

curve shortening flow riemann surfaces conic singularities comparison function gage-hamilton-grayson theorem

Cite

@article{arxiv.2007.00089,
  title  = {Curve shortening flow on Riemann surfaces with possible ambient conic singularities},
  author = {Biao Ma},
  journal= {arXiv preprint arXiv:2007.00089},
  year   = {2022}
}

Comments

31 pages, 4 figures. Accepted version

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