Curve shortening flow on Riemann surfaces with possible ambient conic singularities
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 $\leq \pi$.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2020
- DOI:
- 10.48550/arXiv.2007.00089
- arXiv:
- arXiv:2007.00089
- Bibcode:
- 2020arXiv200700089M
- Keywords:
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- Mathematics - Differential Geometry
- E-Print:
- 31 pages, 4 figures. Accepted version