Calculus of Variations and Geometric Measure Theory

A. Lemenant

Rectifiability of non Euclidean planar self-contracted curves

created by lemenant on 30 Mar 2016



Inserted: 30 mar 2016
Last Updated: 30 mar 2016

Year: 2016


We prove that any self-contracted curve in $\mathbb{R}^2$ 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 $\mathbb{R}^2$ for a general norm together with an adaptation of the argument used in a previous paper by the same author with A. Daniilidis, G. David and E. Durand-Cartagena.