Curve shortening flow on Riemann surfaces with possible ambient conic singularities

2020/06/30 by Biao Ma, Ma, Biao
Mathematics · #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2007.00089

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 ≤ π.

Related

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• Non-uniqueness of curve shortening flow
• The Curve Shortening Flow for Curves of Finite Total (Absolute) Curvature