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 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 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
Classification : 53A04,  37N40,  49J52,  49J53,  52A10,  65K10
Mots clés: Self-contracted curve, uniformly convex norm, rectifiable curve, self-expanded curve, proximal algorithm
     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 = {}
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.

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