27 citations · 29 across the 9 of their papers we have counts for
4 papers · 1 filter
Stratified spaces and synthetic Ricci curvature bounds
J. Bertrand, C Ketterer, Ilaria Mondello +1
We prove that a compact stratied space satises the Riemannian curvature-dimension condition RCD(K, N) if and only if its Ricci tensor is bounded below by K R on the regular s…
DC Calculus
Luigi Ambrosio, Jérôme Bertrand
In this paper, we extend the DC Calculus introduced by Perelman on finite dimensional Alexandrov spaces with curvature bounded below. Among other things, our results allow us to de…
A geometric study of Wasserstein spaces: an addendum on the boundary
Jérôme Bertrand, Benoit Kloeckner
We extend the geometric study of the Wasserstein space W(X) of a simply connected, negatively curved metric space X by investigating which pairs of boundary points can be linked by…
Existence and uniqueness of optimal maps on Alexandrov spaces
Jerome Bertrand
The purpose of this paper is to show that in a finite dimensional metric space with Alexandrov's curvature bounded below, Monge's transport problem for the quadratic cost admits a…