Curvature evolution of plane curves with prescribed opening angle

1995/10/01 by Naoyuki Ishimura · 32 citations
Mathematics · #Center of curvature #Curvature #Geometric Analysis and Curvature Flows #Geometry #Mathematical analysis #Mathematics #Mean curvature #Nonlinear Partial Differential Equations #Plane (geometry) #Plane curve #Point processes and geometric inequalities

paper · pdf · doi:10.1017/s0004972700014714

published in Bulletin of the Australian Mathematical Society 52(2), 287-296 (Cambridge University Press)

openalex publication_date 1995/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We discuss the evolution of plane curves which are described by entire graphs with prescribed opening angle. We show that a solution converges to the unique self-similar solution with the same asymptotics.

Citations

• Sur le mouvement d'un liquide visqueux emplissant l'espace

Cited by

• Volume properties and rigidity on self-expanders of mean curvature flow
• Affine Self-similar solutions of the affine curve shortening flow I: The degenerate case
• A comparison theorem for the isoperimetric profile under curve shortening flow

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