The distance to the boundary with respect to the Minkowski functional of a polytope

2025/12/10 by Mohammad Safdari, Safdari, Mohammad
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2512.10013

openalex publication_date 2025/12/10 · openalex created_date 2025/12/13 · openalex updated_date 2026/07/28

Abstract

We study the regularity of the distance function to the boundary of a domain in ℝⁿ, with respect to the Minkowski functional of a convex polytope. We obtain the regularity of the distance function in certain cases. We also explicitly compute the distance function in a collection of examples and observe the new interesting phenomena that arise for such distance functions.

Citations

• The distance function to the boundary, Finsler geometry and the singular set of viscosity solutions of some Hamilton-Jacobi equations

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