206 citations · 1.5k across the 62 of their papers we have counts for
19 papers · 1 filter
On the rectifiability of and spaces with unique tangents
Mattia Magnabosco, Andrea Mondino, Tommaso Rossi
We prove rectifiability results for and metric measure spaces with pointwise Ahlfors regular reference…
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…
Entropy-Transport distances between unbalanced metric measure spaces
Nicoló De Ponti, Andrea Mondino
Inspired by the recent theory of Entropy-Transport problems and by the -distance of Sturm on normalised metric measure spaces, we define a new class of complete and sep…
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…
On the topology and the boundary of N-dimensional RCD(K,N) spaces
Vitali Kapovitch, Andrea Mondino
We establish topological regularity and stability of N-dimensional RCD(K,N) spaces (up to a small singular set), also called non-collapsed RCD(K,N) in the literature. We also intro…
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…
On quotients of spaces with Ricci curvature bounded below
Fernando Galaz-García, Martin Kell, Andrea Mondino +1
Let be a smooth Riemannian manifold and a compact Lie group acting on effectively and by isometries. It is well known that a lower bound of the sectional c…
Angles between curves in metric measure spaces
Bang-Xian Han, Andrea Mondino
The goal of the paper is to study the angle between two curves in the framework of metric (and metric measure) spaces. More precisely, we give a new notion of angle between two cur…
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…
On the volume measure of non-smooth spaces with Ricci curvature bounded below
Martin Kell, Andrea Mondino
We prove that, given an -space , then it is possible to -essentially cover by measurable subsets with the following proper…
On the universal cover and the fundamental group of an -space
Andrea Mondino, Guofang Wei
The main goal of the paper is to prove the existence of the universal cover for -spaces. This generalizes earlier work of C. Sormani and the second named author on the…
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…
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…
Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
Nicola Gigli, Andrea Mondino, Giuseppe Savaré
Aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition. We propose various definitions, show that all of them are equi…
Euclidean spaces as weak tangents of infinitesimally Hilbertian metric spaces with Ricci curvature bounded below
Nicola Gigli, Andrea Mondino, Tapio Rajala
We show that in any infinitesimally Hilbertian -space at almost every point there exists a Euclidean weak tangent, i.e. there exists a sequence of dilations of the space…
A new notion of angle between three points in a metric space
Andrea Mondino
We give a new notion of angle in general metric spaces; more precisely, given a triple a points in a metric space , we introduce the notion of angle cone ${\angle_{p…
A PDE approach to nonlinear potential theory in metric measure spaces
Nicola Gigli, Andrea Mondino
We show that the tools recently introduced by the first author in [9] allow to give a PDE description of p-harmonic functions in metric measure setting. Three applications are give…