3 papers
math.DG2026
A singularity theorem in terms of asymptotic expansion
Fabio Cavalletti, Andrea Mondino
We prove a singularity theorem in which the classical focusing hypothesis of Hawking--Penrose theory is replaced by a condition on asymptotic volume growth. Under the strong energy…
math.SP2025
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…
math.DG2025
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…