25 citations · 76 across the 13 of their papers we have counts for
7 papers · 1 filter
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…
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…
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…
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 $\&…
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…