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- W4383860623 abstract "In their seminal work, Cordero-Erausquin, Nazaret and Villani [Adv. Math., 2004] proved sharp Sobolev inequalities in Euclidean spaces via Optimal Mass Transportation, raising the question whether their approach is powerful enough to produce sharp Sobolev inequalities also on Riemannian manifolds. In this paper we affirmatively answer their question for Riemannian manifolds with non-negative Ricci curvature; namely, by using Optimal Mass Transportation with quadratic distance cost, sharp $L^p$-Sobolev and $L^p$-logarithmic Sobolev inequalities (both for $p>1$ and $p=1$) are established, where the optimal constants contain the asymptotic volume growth arising from precise asymptotic properties of the Talentian and Gaussian bubbles. As a byproduct, we give an alternative, elementary proof to the main result of do Carmo and Xia [Compos. Math., 2004] (and subsequent results) concerning the quantitative volume non-collapsing estimates on Riemannian manifolds with non-negative Ricci curvature that support certain Sobolev inequalities." @default.
- W4383860623 created "2023-07-11" @default.
- W4383860623 creator A5069656791 @default.
- W4383860623 date "2023-07-07" @default.
- W4383860623 modified "2023-09-27" @default.
- W4383860623 title "Sharp Sobolev inequalities on Riemannian manifolds with ${sf Ric}geq 0$ via Optimal Mass Transportation" @default.
- W4383860623 doi "https://doi.org/10.48550/arxiv.2307.03527" @default.
- W4383860623 hasPublicationYear "2023" @default.
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