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math.AP2024
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…
math.AP2024
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…
math.AP2024
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…