文献类型：期刊文献

英文题名：Failure of famous functional inequalities on Finsler manifolds: the influence of S-curvature

作者：Kristaly, Alexandru[1,2];Li, Benling[3];Zhao, Wei[4]

机构：[1]Babes Bolyai Univ, Dept Econ, Cluj Napoca 400591, Romania;[2]Obuda Univ, Inst Appl Math, H-1034 Budapest, Hungary;[3]Ningbo Univ, Sch Math & Stat, Ningbo 315211, Peoples R China;[4]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2026

卷号：313

期号：4

外文期刊名：MATHEMATISCHE ZEITSCHRIFT

收录：;Scopus(收录号：2-s2.0-105045655755);WOS:【SCI-EXPANDED(收录号:WOS:001831100700002)】；

语种：英文

外文关键词：Finsler manifold; S-curvature; Flag curvature; Ricci curvature; Reversibility; Functional inequalities

摘要：The validity of functional inequalities on Finsler metric measure manifolds is based on three non-Riemannian quantities, namely, the reversibility, flag curvature and S-curvature induced by the measure. Under mild assumptions on the reversibility and flag curvature, it turned out that famous functional inequalities-as Hardy inequality, Heisenberg-Pauli-Weyl uncertainty principle and Caffarelli-Kohn-Nirenberg inequality-usually hold on forward complete Finsler manifolds with non-positive S-curvature. In this paper however we prove that-under similar assumptions on the reversibility and flag curvature as before-the aforementioned functional inequalities fail whenever the S-curvature is positive. Accordingly, our results clearly reveal the deep dependence of functional inequalities on the S-curvature. As a consequence of these results, we establish analytic aspects of Finsler manifolds, e.g., if the flag curvature is non-positive, the Ricci curvature is bounded from below and the S-curvature is positive, then the reversibility turns out to be infinite. Further topological properties and examples are presented on general Funk metric spaces, where the S-curvature plays again a decisive role.