2 citations · 2 across the 3 of their papers we have counts for
8 papers
Geometry of Grassmannians and optimal transport of quantum states
Paolo Antonini, Fabio Cavalletti
Let be a separable Hilbert space. We prove that the Grassmannian of the finite dimensional subspaces of is an Alexandrov space…
Indeterminacy estimates and the size of nodal sets in singular spaces
Fabio Cavalletti, Sara Farinelli
We obtain the sharp version of the uncertainty principle recently introduced in [47], and improved by [13], relating the size of the zero set of a continuous function having zero m…
Displacement convexity of Entropy and the distance cost Optimal Transportation
Fabio Cavalletti, Nicola Gigli, Flavia Santarcangelo
During the last decade Optimal Transport had a relevant role in the study of geometry of singular spaces that culminated with the Lott-Sturm-Villani theory. The latter is built on…
Isoperimetric inequality under Measure-Contraction property
Fabio Cavalletti, Flavia Santarcangelo
We prove that if is an essentially non-branching metric measure space with , having Ricci curvature bounded from below by and dime…
An overview of L1 Optimal Transportation on metric measure spaces
Fabio Cavalletti
The scope of this note is to make a self-contained survey of the recent developments and achievements of the theory of L1-Optimal Transportation on metric measure spaces. Among the…
New formulas for the Laplacian of distance functions and applications
Fabio Cavalletti, Andrea Mondino
The goal of the paper is to prove an exact representation formula for the Laplacian of the distance (and more generally for an arbitrary 1-Lipschitz function) in the framework of m…