# CONFLUENTES MATHEMATICI

Rectifiability of non Euclidean planar self-contracted curves
Confluentes Mathematici, Tome 8 (2016) no. 2, pp. 23-38.

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].

Reçu le : 2016-03-29
Révisé le : 2016-08-24
Accepté le : 2016-08-31
Publié le : 2017-03-20
DOI : https://doi.org/10.5802/cml.31
Classification : 53A04,  37N40,  49J52,  49J53,  52A10,  65K10
Mots clés: Self-contracted curve, uniformly convex norm, rectifiable curve, self-expanded curve, proximal algorithm
@article{CML_2016__8_2_23_0,
author = {Antoine Lemenant},
title = {Rectifiability of non Euclidean planar self-contracted curves},
journal = {Confluentes Mathematici},
publisher = {Institut Camille Jordan},
volume = {8},
number = {2},
year = {2016},
pages = {23-38},
doi = {10.5802/cml.31},
language = {en},
url = {cml.centre-mersenne.org/item/CML_2016__8_2_23_0/}
}
Lemenant, Antoine. Rectifiability of non Euclidean planar self-contracted curves. Confluentes Mathematici, Tome 8 (2016) no. 2, pp. 23-38. doi : 10.5802/cml.31. https://cml.centre-mersenne.org/item/CML_2016__8_2_23_0/

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