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gromov-hausdorff convergence 1heat flow 1optimal transport 1ricci curvature 1weak gradients 1

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math.AP2025

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…

math.AP2025

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…

math.AP2025

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

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…