96 citations · 386 across the 22 of their papers we have counts for
32 papers
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…
Isoperimetric inequality in noncompact MCP spaces
Fabio Cavalletti, Davide Manini
We prove a sharp isoperimetric inequality for the class of metric measure spaces verifying the synthetic Ricci curvature lower bounds and having Euclidean volume growth…
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…
Independence of synthetic Curvature Dimension conditions on transport distance exponent
Afiny Akdemir, Fabio Cavalletti, Andrew Colinet +2
The celebrated Lott-Sturm-Villani theory of metric measure spaces furnishes synthetic notions of a Ricci curvature lower bound joint with an upper bound on the dimension. T…
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…
Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications
Fabio Cavalletti, Andrea Mondino
The goal of the present work is three-fold. The first goal is to set foundational results on optimal transport in Lorentzian (pre-)length spaces, including cyclical monotonicity, s…
Quantitative Obata's Theorem
Fabio Cavalletti, Andrea Mondino, Daniele Semola
We prove a quantitative version of Obata's Theorem involving the shape of functions with null mean value when compared with the cosine of distance functions from single points. The…
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…
Almost euclidean Isoperimetric Inequalities in spaces satisfying local Ricci curvature lower bounds
Fabio Cavalletti, Andrea Mondino
Motivated by Perelman's Pseudo Locality Theorem for the Ricci flow, we prove that if a Riemannian manifold has Ricci curvature bounded below in a metric ball which moreover has alm…
Rigidity for critical points in the Levy-Gromov inequality
Fabio Cavalletti, Francesco Maggi, Andrea Mondino
The Levy-Gromov inequality states that round spheres have the least isoperimetric profile (normalized by total volume) among Riemannian manifolds with a fixed positive lower bound…
The Globalization Theorem for the Curvature Dimension Condition
Fabio Cavalletti, Emanuel Milman
The Lott-Sturm-Villani Curvature-Dimension condition provides a synthetic notion for a metric-measure space to have Ricci-curvature bounded from below and dimension bounded from ab…
Isoperimetric inequalities for finite perimeter sets under lower Ricci curvature bounds
Fabio Cavalletti, Andrea Mondino
We prove that the results regarding the Isoperimetric inequality and Cheeger constant formulated in terms of the Minkowski content, obtained by the authors in previous papers in th…
Optimal maps in essentially non-branching spaces
Fabio Cavalletti, Andrea Mondino
In this note we prove that in a metric measure space verifying the measure contraction property with parameters and , any optimal trans…
Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds
Fabio Cavalletti, Andrea Mondino
For metric measure spaces verifying the reduced curvature-dimension condition we prove a series of sharp functional inequalities under the additional assumption of esse…
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…
Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds
Fabio Cavalletti, Andrea Mondino
We prove that if is a metric measure space with having (in a synthetic sense) Ricci curvature bounded from below by and dime…
Measure rigidity of Ricci curvature lower bounds
Fabio Cavalletti, Andrea Mondino
The measure contraction property, for short, is a weak Ricci curvature lower bound conditions for metric measure spaces. The goal of this paper is to understand whic…
A variational time discretization for the compressible Euler equations
Fabio Cavalletti, Marc Sedjro, Michael Westdickenberg
We introduce a variational time discretization for the multi-dimensional gas dynamics equations, in the spirit of minimizing movements for curves of maximal slope. Each timestep re…
A Simple Proof of Global Existence for the 1D Pressureless Gas Dynamics Equations
Fabio Cavalletti, Marc Sedjro, Michael Westdickenberg
Sticky particle solutions to the one-dimensional pressureless gas dynamics equations can be constructed by a suitable metric projection onto the cone of monotone maps, as was shown…
Monge problem in metric measure spaces with Riemannian curvature-dimension condition
Fabio Cavalletti
We prove the existence of solutions for the Monge minimization problem, addressed in a metric measure space enjoying the Riemannian curvature-dimension condition $\RCD(K,…
A note on a residual subset of Lipschitz functions on metric spaces
Fabio Cavalletti
Let (X, d) be a quasi-convex, complete and separable metric space with reference probability measure m. We prove that the set of of real valued Lipschitz function with non zero poi…