Sobolev Inequalities in Manifolds with Nonnegative Curvature

DOI10.1002/cpa.22070zbMath1527.53030arXiv2009.13717OpenAlexW3093283639WikidataQ125936826 ScholiaQ125936826MaRDI QIDQ6049731

Simon Brendle

Publication date: 11 October 2023

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.13717

zbMATH Keywords

Sobolev inequalitynonnegative Ricci curvatureMichael-Simon inequalityasymptotic volume ratio

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

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Area-minimizing hypersurfaces in manifolds of Ricci curvature bounded below ⋮ Comparison results for solutions of Poisson equations with Robin boundary on complete Riemannian manifolds ⋮ The log-Sobolev inequality for a submanifold in manifolds with asymptotic non-negative intermediate Ricci curvature ⋮ Sobolev inequalities in manifolds with nonnegative intermediate Ricci curvature ⋮ Talenti's comparison theorem for Poisson equation and applications on Riemannian manifold with nonnegative Ricci curvature ⋮ Diameter estimates for submanifolds in manifolds with nonnegative curvature ⋮ Optimal transport approach to Michael-Simon-Sobolev inequalities in manifolds with intermediate Ricci curvature lower bounds ⋮ Sharp log-Sobolev inequalities in \(\mathsf{CD}(0, N)\) spaces with applications ⋮ The Cheeger problem in abstract measure spaces

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