Huang, L., Kristály, Al. & Zhao, W. (2020) Transactions of the American Mathematical Society
Ovidiu Ioan Moisescu
15 Ianuarie 2021
Huang, L., Kristály, Al. & Zhao, W. (2020) Sharp uncertainty principles on general Finsler manifolds. Transactions of the American Mathematical Society, 373(11), 8127-8161.
✓ Publisher: American Mathematical Society
✓ Web of Science Core Collection: Science Citation Index Expanded
✓ Categories: Mathematics
✓ Article Influence Score (AIS): 1.706 (2017) / Q1
Abstract: 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.
inapoi la stiri