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Antoine Lemenant
Rectifiability of non Euclidean planar self-contracted curves
Confluentes Mathematici, 8 no. 2 (2016), p. 23-38, doi: 10.5802/cml.31
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Class. Math.: 53A04, 37N40, 49J52, 49J53, 52A10, 65K10
Keywords: Self-contracted curve, uniformly convex norm, rectifiable curve, self-expanded curve, proximal algorithm

Résumé - Abstract

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 [2].


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