文献类型：期刊文献

英文题名：Sharp Hardy Inequalities via Riemannian Submanifolds

作者：Chen, Yunxia[1];Leung, Naichung Conan[2,3];Zhao, Wei[1]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai, Peoples R China;[2]Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China;[3]Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

年份：2022

卷号：32

期号：7

外文期刊名：JOURNAL OF GEOMETRIC ANALYSIS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000800856400003)】；

基金：This work was supported by National Natural Science Foundation of China (No. 11761058) and Natural Science Foundation of Shanghai (Nos. 19ZR1411700, 21ZR1418300).

语种：英文

外文关键词：Hardy inequality; Optimal constant; Minimal submanifold; Weak mean convexity; Ricci curvature; Fermi coordinates

摘要：This paper is devoted to Hardy inequalities concerning distance functions from submanifolds of arbitrary codimensions in the Riemannian setting. On a Riemannian manifold with non-negative curvature, we establish several sharp weighted Hardy inequalities in the cases when the submanifold is compact as well as non-compact. In particular, these inequalities remain valid even if the ambient manifold is compact, in which case we find an optimal space of smooth functions to study Hardy inequalities. Further examples are also provided. Our results complement in several aspects those obtained recently in the Euclidean and Riemannian settings.