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Rectifiability of non Euclidean planar self-contracted curves
Antoine Lemenant1
1 Université Paris Diderot – Paris 7, CNRS, UMR 7598 Laboratoire Jacques-Louis Lions, Paris, F-75005, France
Confluentes Mathematici, Volume 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].

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Published online:
DOI: 10.5802/cml.31
Classification: 53A04, 37N40, 49J52, 49J53, 52A10, 65K10
Keywords: Self-contracted curve, uniformly convex norm, rectifiable curve, self-expanded curve, proximal algorithm

Antoine Lemenant 1

1 Université Paris Diderot – Paris 7, CNRS, UMR 7598 Laboratoire Jacques-Louis Lions, Paris, F-75005, France 
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Antoine Lemenant. Rectifiability of non Euclidean planar self-contracted curves. Confluentes Mathematici, Volume 8 (2016) no. 2, pp. 23-38. doi : 10.5802/cml.31. https://cml.centre-mersenne.org/articles/10.5802/cml.31/

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