3 papers
math.DG2026
New Topological Restrictions For Spaces With Nonnegative Ricci Curvature
Alessandro Cucinotta, Mattia Magnabosco, Daniele Semola
We obtain new topological restrictions for complete Riemannian manifolds with nonnegative Ricci curvature and RCD(0,n) spaces. Our main results are a Betti number rigidity theorem…
math.DG2025
On perimeter minimizing sets in manifolds with quadratic volume growth
Alessandro Cucinotta, Mattia Magnabosco
This paper studies whether the presence of a perimeter minimizing set in a Riemannian manifold forces an isometric splitting. We show that this is the case when has non…
math.DG2025
On manifolds with almost non-negative Ricci curvature and integrally-positive -scalar curvature
Alessandro Cucinotta, Andrea Mondino
We consider manifolds with almost non-negative Ricci curvature and strictly positive integral lower bounds on the sum of the lowest eigenvalues of the Ricci tensor. If $(M^n,g)…