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Weighted Poincar\'e inequality and its applications on Finsler manifolds
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In this note, we present several generalized Poincar\'e inequalities on Finsler metric measure manifolds. As applications, we prove the general Sobolev inequality and the general Nash inequality on Finsler manifolds with certain conditions.
Abstract
In this note, we present several generalized Poincar\'e inequalities on Finsler metric measure manifolds. As applications, we prove the general Sobolev inequality and the general Nash inequality on Finsler manifolds with certain conditions.
관련 논문AI추천
The Hardy type inequality on metric measure spacesChuanxi Wu, Feng Du, Jing Mao, Qiaoling Wang대한수학회 · 대한수학회지2018 · 제55권 제6호SOME INTEGRAL INEQUALITIES FOR THE LAPLACIAN WITH DENSITY ON WEIGHTED MANIFOLDS WITH BOUNDARYFanqi Zeng대한수학회 · 대한수학회보2023 · 제60권 제2호COMPARISON THEOREMS IN FINSLER GEOMETRY WITH WEIGHTED CURVATURE BOUNDS AND RELATED RESULTSBing-Ye Wu대한수학회 · 대한수학회지2015 · 제52권 제3호Generalized Myers theorem for Finsler manifolds with integral Ricci curvature boundBing-Ye Wu대한수학회 · 대한수학회보2019 · 제56권 제4호Comparison theorems in Riemann-Finsler geometry with line radial integral curvature bounds and related resultsBing-Ye Wu대한수학회 · 대한수학회지2019 · 제56권 제2호Rigidity theorems of some dually flat Finsler metrics and its applicationsBin Shen, Yanfang Tian대한수학회 · 대한수학회보2016 · 제53권 제5호
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