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Hardy type inequalities on closed manifolds via Ricci curvature

Part of: Inequalities Global differential geometry

Published online by Cambridge University Press:  21 July 2020

Canjun Meng ,
Han Wang  and
Wei Zhao
Canjun Meng
Affiliation:
Department of Mathematics, East China University of Science and Technology, Shanghai200237, China (10173968@mail.ecust.edu.cn; 10172443@mail.ecust.edu.cn; szhao_wei@yahoo.com, wzhao@ecust.edu.cn)
Han Wang
Affiliation:
Department of Mathematics, East China University of Science and Technology, Shanghai200237, China (10173968@mail.ecust.edu.cn; 10172443@mail.ecust.edu.cn; szhao_wei@yahoo.com, wzhao@ecust.edu.cn)
Wei Zhao
Affiliation:
Department of Mathematics, East China University of Science and Technology, Shanghai200237, China (10173968@mail.ecust.edu.cn; 10172443@mail.ecust.edu.cn; szhao_wei@yahoo.com, wzhao@ecust.edu.cn)
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Abstract

The article is devoted to Hardy type inequalities on closed manifolds. By means of various weighted Ricci curvatures, we establish several sharp Hardy type inequalities on closed weighted Riemannian manifolds. Our results complement in several aspects those obtained recently in the non-compact Riemannian setting.

Keywords

Hardy inequalitybest constantclosed manifoldweighted Ricci curvatureweighted Riemannian manifoldp-Laplacian

MSC classification

Primary: 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 3 , June 2021 , pp. 993 - 1020
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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