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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.DG2023
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…