文献类型：期刊文献

英文题名：SHARP UNCERTAINTY PRINCIPLES ON GENERAL FINSLER MANIFOLDS

作者：Huang, Libing[1,2];Kristaly, Alexandru[3,4];Zhao, Wei[5]

机构：[1]Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China;[2]Nankai Univ, LPMC, Tianjin 300071, Peoples R China;[3]Babes Bolyai Univ, Dept Econ, Cluj Napoca 400591, Romania;[4]Obuda Univ, Inst Appl Math, H-1034 Budapest, Hungary;[5]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2020

卷号：373

期号：11

起止页码：8127

外文期刊名：TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000588753400018)】；

基金：The research of the second author was supported by the National Research, Development and Innovation Fund of Hungary, financed under the K 18 funding scheme, Project no. 127926.r The third author was supported by the National Natural Science Foundation of China (No. 11501202, No. 11761058) and the grant of China Scholarship Council (No. 201706745006).

语种：英文

外文关键词：Uncertainty principles; Caffarelli-Kohn-Nirenberg interpolation inequality; Heisenberg-Pauli-Weyl inequality; Hardy inequality; Finsler manifold; reversibility; sharp constant; rigidity

摘要：The paper is devoted to sharp uncertainty principles (Heisenberg-Pauli-Weyl, Caffarelli-Kohn-Nirenberg, and Hardy inequalities) on forward complete Finsler manifolds endowed with an arbitrary measure. Under mild assumptions, the existence of extremals corresponding to the sharp constants in the Heisenberg-Pauli-Weyl and Caffarelli-Kohn-Nirenberg inequalities fully characterizes the nature of the Finsler manifold in terms of three non-Riemannian quantities, namely, its reversibility and the vanishing of the flag curvature and S-curvature induced by the measure, respectively. It turns out in particular that the Busemann-Hausdorff measure is the optimal one in the study of sharp uncertainty principles on Finsler manifolds. The optimality of our results are supported by Randers-type Finslerian examples originating from the Zermelo navigation problem.