25 citations · 76 across the 13 of their papers we have counts for
14 papers
A singularity theorem in terms of asymptotic expansion
Fabio Cavalletti, Andrea Mondino
We prove a sharp singularity theorem in which the classical focusing hypothesis of Hawking--Penrose theory is replaced by a condition on the asymptotic volume growth of timelike ge…
Cheng's eigenvalue comparison on metric measure spaces and applications
G. Bruno De Luca, Nicolò De Ponti, Andrea Mondino +1
Using the localization technique, we prove a sharp upper bound on the first Dirichlet eigenvalue of metric balls in essentially non-branching spaces. Thi…
Can you hear the Planck mass?
G. Bruno De Luca, Nicolò De Ponti, Andrea Mondino +1
For the Laplacian of an -Riemannian manifold , the Weyl law states that the -th eigenvalue is asymptotically proportional to , where is the volume of .…
Monotonicity formula and stratification of the singular set of perimeter minimizers in RCD spaces
Francesco Fiorani, Andrea Mondino, Daniele Semola
The goal of this paper is to establish a monotonicity formula for perimeter minimizing sets in RCD(0,N) metric measure cones, together with the associated rigidity statement. The a…
Harmonic functions and gravity localization
G. Bruno De Luca, Nicolò De Ponti, Andrea Mondino +1
In models with extra dimensions, matter particles can be easily localized to a 'brane world', but gravitational attraction tends to spread out in the extra dimensions unless they a…
On the notion of Laplacian bounds on spaces and applications
Nicola Gigli, Andrea Mondino, Daniele Semola
We show that several different interpretations of the inequality are equivalent in the setting of spaces. With respect to previously available results…
Gravity from thermodynamics: optimal transport and negative effective dimensions
G. Bruno De Luca, Nicolò De Ponti, Andrea Mondino +1
We prove an equivalence between the classical equations of motion governing vacuum gravity compactifications (and more general warped-product spacetimes) and a concavity property o…
Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures
Davide Barilari, Andrea Mondino, Luca Rizzi
Recent advances in the theory of metric measures spaces on the one hand, and of sub-Riemannian ones on the other hand, suggest the possibility of a "great unification" of Riemannia…
The metric measure boundary of spaces with Ricci curvature bounded below
Elia Bruè, Andrea Mondino, Daniele Semola
We solve a conjecture raised by Kapovitch, Lytchak, and Petrunin by showing that the metric measure boundary is vanishing on any space without boundary. Our result…
A review of Lorentzian synthetic theory of timelike Ricci curvature bounds
Fabio Cavalletti, Andrea Mondino
The scope of this survey is to give a self-contained introduction to synthetic timelike Ricci curvature bounds for (possibly non-smooth) Lorentzian spaces via optimal transport $\&…
Moduli spaces of compact RCD(0,N)-structures
Andrea Mondino, Dimitri Navarro
The goal of the paper is to set the foundations and prove some topological results about moduli spaces of non-smooth metric measure structures with non-negative Ricci curvature in…
Quantization of the Willmore Energy in Riemannian Manifolds
Alexis Michelat, Andrea Mondino
We show that the quantization of energy for Willmore spheres into closed Riemannian manifolds holds provided that the Willmore energy and the area are uniformly bounded. The analog…
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…
Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds II: Morse Theory
Norihisa Ikoma, Andrea Malchiodi, Andrea Mondino
This is the second of a series of two papers where we construct embedded Willmore tori with small area constraint in Riemannian three-manifolds. In both papers the construction rel…