Ancient Solutions to Curve Shortening with Finite Total Curvature

2018/03/04 by Sigurd Angenent, Angenent, Sigurd, You Qian +1 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Mathematics and Applications #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1803.01399

Abstract

We construct ancient solutions to Curve Shortening in the plane whose total curvature is uniformly bounded by gluing together an arbitrary chain of given Grim Reapers along their common asymptotes.

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