文献类型：期刊文献

英文题名：Sharp Hardy Inequalities Involving Distance Functions From Submanifolds of Riemannian Manifolds

作者：Cui, Ningwei[1];Kristaly, Alexandru[2,3];Zhao, Wei[4]

机构：[1]Southwest Jiaotong Univ, Sch Math, Chengdu 610031, Peoples R China;[2]Babes Bolyai Univ, Dept Econ, Cluj Napoca 400591, Romania;[3]Obuda Univ, Inst Appl Math, H-1034 Budapest, Hungary;[4]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2025

卷号：35

期号：12

外文期刊名：JOURNAL OF GEOMETRIC ANALYSIS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001584793600001)】；

基金：A. Kristaly is supported by the Excellence Researcher Program OE-KP-2-2022 of Obuda University, Hungary. W. Zhao is supported by Natural Science Foundation of China (No. 12471045), Ningbo Natural Science Foundation (No. 2024J017) and Science and Technology Project of Xinjiang Production and Construction Corps (No. 2023CB008-12).

语种：英文

外文关键词：Riemannian manifolds; Submanifolds; Curvature; Hardy inequality

摘要：We establish various Hardy inequalities involving the distance function from submanifolds of Riemannian manifolds, where the natural weights are expressed in terms of bounds of the mean curvature of the submanifold and sectional/Ricci curvature of the ambient Riemannian manifold. Our approach is based on subtle Heintze-Karcher-type Laplace comparisons of the distance function and on a D'Ambrosio-Dipierro-type weak divergence formula for suitable vector fields, providing Barbatis-Filippas-Tertikas-type Hardy inequalities in the curved setting. Under very mild assumptions, we also establish the sharpness and non-existence of extremal functions within the Hardy inequalities and - depending on the geometry of the ambient manifold - their extensibility to various function spaces. Several examples are provided by showing the applicability of our approach; in particular, well-known Hardy inequalities appear as limit cases of our new inequalities.