32 citations · 194 across the 33 of their papers we have counts for
5 papers · 1 filter
Coloring distance graphs: a few answers and many questions
Benoît Kloeckner
Given a metric space and a set of distances, one constructs the associated distance graph by taking as vertices the points of the space and as edges the pairs whose distance is in…
A geometric study of Wasserstein spaces: ultrametrics
Benoît Kloeckner
We study the geometry of the space of measures of a compact ultrametric space X, endowed with the L^p Wasserstein distance from optimal transportation. We show that the power p of…
The Cartan-Hadamard conjecture and The Little Prince
Benoît Kloeckner, Greg Kuperberg
The generalized Cartan-Hadamard conjecture says that if is a domain with fixed volume in a complete, simply connected Riemannian -manifold with sectional curvature $K \l…
Yet another short proof of Bourgain's distorsion estimate
Benoît Kloeckner
We use a self-improvement argument to give a very short and elementary proof of the result of Bourgain saying that regular trees do not admit bi-Lipschitz embeddings into uniformly…
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…