Biao Ma — Neckpinchhttps://neckpinch.com/authors/biao-ma/New arXiv papers by Biao Ma, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT Curve shortening flow on Riemann surfaces with possible ambient conic singularitieshttps://neckpinch.com/papers/2007.00089/arxiv:2007.00089Tue, 30 Jun 2020 00:00:00 GMTBiao Ma — 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.Curve shorteningSingularitiesSurfaces