From the 1 of 7 linked papers with an AI index.
7 papers
A splitting theorem for manifolds with a convex boundary component and applications
Alessandro Cucinotta, Andrea Mondino
The paper proves a warped‑product splitting theorem for manifolds with a convex, parabolic boundary component under Ricci curvature lower bounds, and uses it to obtain splitting an…
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)…
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…
Half Space Property in RCD(K,N) spaces
Alessandro Cucinotta, Andrea Mondino
The goal of this note is to prove the Half Space Property for RCD(0,N) spaces, namely that if (X,d,m) is a parabolic RCD(0,N) space and is locally…
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…
Minimal Surface Equation and Bernstein Property on RCD spaces
Alessandro Cucinotta
We show that if is an RCD(K,N) space and is a solution of the minimal surface equation, then is harmonic on its graph (which has a natural me…