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…
hep-th2024
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 .…