Calculus of Variations and Geometric Measure Theory

A. Figalli - N. Juillet

Absolute continuity of Wasserstein geodesics in the Heisenberg group

created by figalli on 04 Apr 2008
modified on 28 Nov 2008


Accepted Paper

Inserted: 4 apr 2008
Last Updated: 28 nov 2008

Journal: J. Funct. Anal.
Year: 2008


In this paper we answer to a question raised by Ambrosio and Rigot proving that any interior point of a Wasserstein geodesic in the Heisenberg group is absolutely continuous if one of the end-points is. Since our proof relies on the validity of the so-called Measure Contraction Property and on the fact that the optimal transport map exists and the Wasserstein geodesic is unique, the absolute continuity of Wasserstein geodesic also holds for Alexandrov spaces with curvature bounded from below.