Sharp distance comparison for curve shortening flow on the round sphere

2023/10/04 by Paul Bryan, Bryan, Paul, Mat Langford +3 · 1 citation
Earth and Planetary Sciences · Mathematics · #53E10 #Differential Geometry (math.DG) #FOS: Mathematics #Geological formations and processes #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2310.02649

openalex publication_date 2023/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that curve shortening flow on the round sphere displays sharp chord-arc improvement, precisely as in the planar setting (Andrews and Bryan, Comm. Anal. Geom., 2011). As in the planar case, the sharp estimate implies control on the curvature, resulting in a direct and efficient proof that simple spherical curves either contract to round points (in finite time) or converge to great circles (in infinite time).

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• Huisken's Distance Comparison Principle in Higher Codimension

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