8 papers
Divergence-free concentrations come from vanishing sequences
Adolfo Arroyo-Rabasa, Francesco Nobili, Ivan Yuri Violo
A vanishing sequence of divergence-free matrix fields is one that is bounded in and is carried by open sets of vanishing volume. Recently established, Bouchitté's…
Stability of local Riemannian Ricci curvature lower bounds
Luigi Ambrosio, Francesco Nobili, Federico Renzi +1
We establish the stability of local Riemannian Ricci curvature lower bounds along Gromov-Hausdorff convergence. A central part of our analysis is devoted to showing the stability o…
Mosco-convergence of Cheeger energies on varying spaces satisfying curvature dimension conditions
Francesco Nobili, Federico Renzi, Federico Vitillaro
We study the Mosco-convergence of Cheeger energies on Gromov-Hausdorff converging spaces satisfying different types of curvature dimension conditions. The case of functions of boun…
Comparison estimates on nonsmooth spaces with integrable Ricci lower bounds via localization
Emanuele Caputo, Francesco Nobili, Tommaso Rossi
We study comparison estimates on metric measure spaces admitting a synthetic variable Ricci curvature lower bound. We obtain geometric and functional inequalities assuming that the…
Generalized existence of extremizers for the sharp -Sobolev inequality on Riemannian manifolds with nonnegative curvature
Francesco Nobili, Ivan Yuri Violo
We study the generalized existence of extremizers for the sharp -Sobolev inequality on noncompact Riemannian manifolds in connection with nonnegative curvature and Euclidean vol…
An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds
Francesco Nobili
We review recent results regarding the problem of the stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds. We shall describe techniques and…
Fine Pólya-Szegő rearrangement inequalities in metric spaces and applications
Francesco Nobili, Ivan Yuri Violo
We study fine Pólya-Szegő rearrangement inequalities into weighted intervals for Sobolev functions and functions of bounded variation defined on metric measure spaces supporting an…
Quantitative stability of Sobolev inequalities on compact Riemannian manifolds
Francesco Nobili, Davide Parise
We study quantitative stability results for different classes of Sobolev inequalities on general compact Riemannian manifolds. We prove that, up to constants depending on the manif…