Rectifiability of non Euclidean planar self-contracted curves

2016/03/31 by Antoine Lemenant, Lemenant, Antoine
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Point processes and geometric inequalities #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1604.02673

openalex publication_date 2016/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that any self-contracted curve in R 2 endowed with a C 2 and strictly convex norm, has finite length. The proof follows from the study of the curve bisector of two points in R 2 for a general norm together with an adaptation of the argument used in [2].

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