文献类型：期刊文献

英文题名：Sharp uncertainty principles on general Finsler manifolds

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

机构：[1] School of Mathematical Sciences, LPMC, Nankai University, Tianjin, 300071, China; [2] Department of Economics, Babe?-Bolyai University, Cluj-Napoca, 400591, Romania; [3] Institute of Applied Mathematics, óbuda University, Budapest, 1034, Hungary; [4] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

年份：2018

外文期刊名：arXiv

收录：EI(收录号：20200623293)

语种：英文

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. Our results complement in several aspects those obtained recently in the Riemannian setting by Kristály [J. Math. Pures Appl. (9) 119 (2018), 326–346], their optimality being supported by Randers-type Finslerian examples originating from the Zermelo navigation problem. Copyright ? 2018, The Authors. All rights reserved.