Rectifiability of non Euclidean planar self-contracted curves
  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]. 
Antoine Lemenant (LJLL)
math.MG