4 citations · 12 across the 16 of their papers we have counts for
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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…
A review of the tangent space in sub-Finsler geometry and applications to the failure of the condition
Mattia Magnabosco, Tommaso Rossi
We review the construction of the tangent space to a sub-Finsler manifold in the measured Gromov-Hausdorff sense. Under suitable assumptions on the measure, the metric measure tang…
The Brunn--Minkowski inequality implies the CD condition in weighted Riemannian manifolds
Mattia Magnabosco, Lorenzo Portinale, Tommaso Rossi
The curvature dimension condition CD(K,N), pioneered by Sturm and Lott--Villani, is a synthetic notion of having curvature bounded below and dimension bounded above, in the non-smo…
Almost-Riemannian manifolds do not satisfy the condition
Mattia Magnabosco, Tommaso Rossi
The Lott-Sturm-Villani curvature-dimension condition provides a synthetic notion for a metric-measure space to have curvature bounded from below by and dimen…
Optimal maps and local-to-global property in negative dimensional spaces with Ricci curvature bounded from below
Mattia Magnabosco, Chiara Rigoni
In this paper we investigate two important properties of metric measure spaces satisfying the reduced curvature-dimension condition for negative values of the dimension parameter:…