2024
DOI: 10.1007/s00526-024-02810-9
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Sharp Sobolev inequalities on noncompact Riemannian manifolds with $$\textsf{Ric}\ge 0$$ via optimal transport theory

Alexandru Kristály

Abstract: In their seminal work, Cordero-Erausquin, Nazaret and Villani (Adv Math 182(2):307-332, 2004) proved sharp Sobolev inequalities in Euclidean spaces via Optimal Transport, raising the question whether their approach is powerful enough to produce sharp Sobolev inequalities also on Riemannian manifolds. By using $$L^1$$ L 1 -optimal transport approach, the compact case has been successfully treated by Cavalletti and Mond… Show more

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