206 citations · 1.5k across the 62 of their papers we have counts for
65 papers
Orientability of metric manifolds and metric spaces with curvature bounds
Nicola Cavallucci, Denis Marti, Andrea Mondino +1
We develop a theory of orientability for metric manifolds and singular metric spaces using locally integral currents. For topological -manifolds with locally finite Hausdorff me…
The Null Energy Condition through the Lens of Optimal Transport: Smooth and Non-Smooth Spacetimes
Fabio Cavalletti, Davide Manini, Andrea Mondino
We survey recent developments on the null energy condition (NEC) from the perspective of optimal transport, with emphasis on non-smooth Lorentzian geometry. After recalling the rol…
Gromov-Hausdorff and intrinsic flat convergence of RCD(K,N) and Kato spaces
Andrea Mondino, Raquel Perales
We consider metric measure spaces satisfying the properties (ETR), (LBD), and with an almost everywhere connected regular set. In particular, these a…
On the geometry of synthetic null hypersurfaces
Fabio Cavalletti, Davide Manini, Andrea Mondino
This paper develops a synthetic framework for the geometric and analytic study of null (lightlike) hypersurfaces in non-smooth spacetimes. Drawing from optimal transport and recent…
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…
Optimal transport on null hypersurfaces and the null energy condition
Fabio Cavalletti, Davide Manini, Andrea Mondino
The goal of the present work is to study optimal transport on null hypersurfaces inside Lorentzian manifolds. The challenge here is that optimal transport along a null hypersurface…
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…
Lipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from spaces to spaces
Andrea Mondino, Daniele Semola
We establish Lipschitz regularity of harmonic maps from metric measure spaces with lower Ricci curvature bounds and dimension upper bounds in synthetic sense wi…
A reverse Hölder inequality for first eigenfunctions of the Dirichlet Laplacian on RCD(K,N) spaces
Mustafa Alper Gunes, Andrea Mondino
In the framework of (possibly non-smooth) metric measure spaces with Ricci curvature bounded below by a positive constant in a synthetic sense, we establish a sharp and rigid rever…
Cheeger bounds on spin-two fields
G. Bruno De Luca, Nicolò De Ponti, Andrea Mondino +1
We consider gravity compactifications whose internal space consists of small bridges connecting larger manifolds, possibly noncompact. We prove that, under rather general assumptio…
Weak Laplacian bounds and minimal boundaries in non-smooth spaces with Ricci curvature lower bounds
Andrea Mondino, Daniele Semola
The goal of the paper is four-fold. In the setting of non-smooth spaces with Ricci curvature lower bounds (more precisely RCD(K,N) metric measure spaces): - we develop an intrinsic…
Some rigidity results for the Hawking mass and a lower bound for the Bartnik capacity
Andrea Mondino, Aidan Templeton-Browne
We prove rigidity results involving the Hawking mass for surfaces immersed in a -dimensional, complete Riemannian manifold with non-negative scalar curvature (resp. with…
An upper bound on the revised first Betti number and a torus stability result for RCD spaces
Ilaria Mondello, Andrea Mondino, Raquel Perales
We prove an upper bound on the rank of the abelianised revised fundamental group (called "revised first Betti number") of a compact space, in the same spirit of the…
A strict inequality for the minimisation of the Willmore functional under isoperimetric constraint
Andrea Mondino, Christian Scharrer
Inspired by previous work of Kusner and Bauer-Kuwert, we prove a strict inequality between the Willmore energies of two surfaces and their connected sum in the context of isoperime…
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…
A Talenti-type comparison theorem for spaces and applications
Andrea Mondino, Mattia Vedovato
We prove pointwise and -gradient comparison results for solutions to elliptic Dirichlet problems defined on open subsets of a (possibly non-smooth) space with positive Ricci…
The equality case in Cheeger's and Buser's inequalities on spaces
Nicolò De Ponti, Andrea Mondino, Daniele Semola
We prove that the sharp Buser's inequality obtained in the framework of spaces by the first two authors is rigid, i.e. equality is obtained if and only if…
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…
Existence and Regularity of Spheres Minimising the Canham-Helfrich Energy
Andrea Mondino, Christian Scharrer
We prove existence and regularity of minimisers for the Canham-Helfrich energy in the class of weak (possibly branched and bubbled) immersions of the -sphere. This solves (the s…
Sharp Cheeger-Buser type inequalities in spaces
Nicolò De Ponti, Andrea Mondino
The goal of the paper is to sharpen and generalise bounds involving the Cheeger's isoperimetric constant and the first eigenvalue of the Laplacian. A celebrated lower b…
An optimal transport formulation of the Einstein equations of general relativity
Andrea Mondino, Stefan Suhr
The goal of the paper is to give an optimal transport formulation of the full Einstein equations of general relativity, linking the (Ricci) curvature of a space-time with the cosmo…
Polya-Szego inequality and Dirichlet -spectral gap for non-smooth spaces with Ricci curvature bounded below
Andrea Mondino, Daniele Semola
We study decreasing rearrangements of functions defined on (possibly non-smooth) metric measure spaces with Ricci curvature bounded below by and dimension bounded above by $N…
Foliation by area-constrained Willmore spheres near a non-degenerate critical point of the scalar curvature
Norihisa Ikoma, Andrea Malchiodi, Andrea Mondino
Let be a 3-dimensional Riemannian manifold. The goal of the paper it to show that if is a non-degenerate critical point of the scalar curvature, then a neighbo…