32 citations · 194 across the 33 of their papers we have counts for
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A geometric study of Wasserstein spaces: isometric rigidity in negative curvature
Jérôme Bertrand, Benoît Kloeckner
Given a metric space X, one defines its Wasserstein space W2(X) as a set of sufficiently decaying probability measures on X endowed with a metric defined from optimal transportatio…
A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces
Benoit Kloeckner
A Wasserstein spaces is a metric space of sufficiently concentrated probability measures over a general metric space. The main goal of this paper is to estimate the largeness of Wa…
A geometric study of Wasserstein spaces: Hadamard spaces
Jérôme Bertrand, Benoît Kloeckner
Optimal transport enables one to construct a metric on the set of (sufficiently small at infinity) probability measures on any (not too wild) metric space X, called its Wasserstein…
On Lipschitz compactifications of trees
Benoit Kloeckner
We study the Lipschitz structures on the geodesic compactification of a regular tree, that are preserved by the automorphism group. They are shown to be similar to the compactifica…
A geometric study of Wasserstein spaces: Euclidean spaces
Benoit Kloeckner
We study the Wasserstein space (with quadratic cost) of Euclidean spaces as an intrinsic metric space. In particular we compute their isometry groups. Surprisingly, in the case of…
On differentiable compactifications of the hyperbolic space
Benoit Kloeckner
The group of direct isometries of the real n-dimensional hyperbolic space is G=SOo(n,1). This isometric action admits many differentiable compactifications into an action on the cl…