2 citations · 2 across the 3 of their papers we have counts for
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A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds
Fabio Cavalletti, Andrea Mondino
The paper establishes a sharp and rigid isoperimetric-type inequality in Lorentzian signature under the assumption of Ricci curvature bounded below in the timelike directions. The…
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…
Tangent lines and Lipschitz differentiability spaces
Fabio Cavalletti, Tapio Rajala
We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces. We first revisit the almost everywhere me…