From the 1 of 6 linked papers with an AI index.
6 papers
Stability of local Riemannian Ricci curvature lower bounds
Luigi Ambrosio, Francesco Nobili, Federico Renzi +1
The paper proves that lower bounds on Ricci curvature for Riemannian manifolds remain stable under Gromov‑Hausdorff convergence, using a local analysis of weak gradients and heat‑f…
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…
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…
Fine Pólya-SzegŠrearrangement inequalities in metric spaces and applications
Francesco Nobili, Ivan Yuri Violo
We study fine Pólya-SzegÅ rearrangement inequalities into weighted intervals for Sobolev functions and functions of bounded variation defined on metric measure spaces supporting…
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…
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…