1 citations · 2 across the 9 of their papers we have counts for
9 papers
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…
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…
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)…
A splitting theorem for manifolds with a convex boundary component and applications
Alessandro Cucinotta, Andrea Mondino
We prove a warped product splitting theorem for manifolds with Ricci curvature bounded from below in the spirit of [Croke-Kleiner, \emph{Duke Math.\;J}.\;(1992)], but instead of as…
On the dimension of the singular set of perimeter minimizers in spaces with a two-sided Ricci curvature bound
Alessandro Cucinotta, Francesco Fiorani
We show that the Hausdorff dimension of the singular set of perimeter minimizers in non-collapsed Ricci limit spaces with a two-sided Ricci curvature bound is at most , where…
Convergence of the area functional on spaces with lower Ricci bounds and applications
Alessandro Cucinotta
We show that the heat flow provides good approximation properties for the area functional on proper $\RCD(K,\infty)$ spaces, implying that in this setting the area formula for func…
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…
On the properties of the set where a generalized function of bounded variation takes infinite value
Alessandro Cucinotta
We study the properties of the set where a generalized function of bounded variation has infinite approximate limit, highlighting in this way the main geometric difference with fun…
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…