Affine Self-similar solutions of the affine curve shortening flow I: The degenerate case

2017/11/24 by Chengjie Yu, Feifei Zhao, Yu, Chengjie +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1711.08872

openalex publication_date 2017/11/24 · openalex created_date 2017/12/04 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider affine self-similar solutions for the affine curve shortening flow in the Euclidean plane. We obtain the equations of all affine self-similar solutions up to affine transformations and solve the equations or give descriptions of the solutions for the degenerate case. Some new special solutions for the affine curve shortening flow are found.

Citations

• An isoperimetric inequality with applications to curve shortening
• Curvature evolution of plane curves with prescribed opening angle

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