552 citations · 2.1k across the 56 of their papers we have counts for
6 papers · 1 filter
A PDE approach to a 2-dimensional matching problem
Luigi Ambrosio, Federico Stra, Dario Trevisan
We prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected quadratic transportati…
Linear extension operators between spaces of Lipschitz maps and optimal transport
Luigi Ambrosio, Daniele Puglisi
Motivated by the notion of K-gentle partition of unity introduced in [12] and the notion of K-Lipschitz retract studied in [17], we study a weaker notion related to the Kantorovich…
Gaussian-type Isoperimetric Inequalities in probability spaces for positive
Luigi Ambrosio, Andrea Mondino
In this paper we adapt the well-estabilished -calculus techniques to the context of spaces, proving Bobkov's local isoperimetric inequality and, when is posi…
New stability results for sequences of metric measure spaces with uniform Ricci bounds from below
Luigi Ambrosio, Shouhei Honda
The aim of this paper is to provide new stability results for sequences of metric measure spaces convergent in the measured Gromov-Hausdorff sense. By adopting the…
Perimeter as relaxed Minkowski content in metric measure spaces
Luigi Ambrosio, Nicola Gigli, Simone Di Marino
In this note we prove that on general metric measure spaces the perimeter is equal to the relaxation of the Minkowski content w.r.t.\ convergence in measure
Weak and strong convergence of derivations and stability of flows with respect to MGH convergence
Luigi Ambrosio, Federico Stra, Dario Trevisan
This paper is devoted to the study of weak and strong convergence of derivations, and of the flows associated to them, when dealing with a sequence of metric measure structures (X,…