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math.MG2016
Rectifiability of non Euclidean planar self-contracted curves
Antoine Lemenant
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…
math.MG2014★ 44 cited
Approximation of length minimization problems among compact connected sets
Matthieu Bonnivard, Antoine Lemenant, Filippo Santambrogio
In this paper we provide an approximation à la Ambrosio-Tortorelli of some classical minimization problems involving the length of an unknown one-dimensional set, with an additiona…