On volume-preserving crystalline mean curvature flow

2020/12/27 by Inwon C. Kim, Kim, Inwon, Dohyun Kwon +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2012.13839

openalex publication_date 2020/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we consider the global existence of volume-preserving crystalline curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address global existence and regularity of the flow for smooth anisotropies. For the non-smooth case we establish global existence results for the types of anisotropies known to be globally well-posed.

Citations

• Existence and uniqueness for planar anisotropic and crystalline\n curvature flow
• Existence and uniqueness for anisotropic and crystalline mean curvature flows

Cited by

• Bubbling of almost critical points of anisotropic isoperimetric problems with degenerating ellipticity

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