2018/11/21 by Libing Huang, Alexandru Kristály, Huang, Libing +3 · 1 citation
Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1811.08697
openalex publication_date 2018/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.