Blow-up rates for the general curve shortening flow

2009/08/13 by Rongli Huang, Huang, Rongli, Juanjuan Chen +1
Mathematics · #35k45 #35k65 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.AP #math.DG #msc:35k45 #msc:35k65

paper · pdf · doi:10.48550/arxiv.0908.1885

12pages

openalex publication_date 2009/08/13 · arxiv created 2010/01/19 · arxiv updated 2010/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The blow-up rates of derivatives of the curvature function will be presented when the closed curves contract to a point in finite time under the general curve shortening flow. In particular, this generalizes a theorem of M.E. Gage and R.S. Hamilton about mean curvature flow in ℝ².

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