文献类型：期刊文献

英文题名：Unexpected analytic phenomena on Finsler manifolds

作者：Li, Benling[1];Zhao, Wei[2]

机构：[1]Ningbo Univ, Sch Math & Stat, Ningbo 315211, Peoples R China;[2]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2026

卷号：481

外文期刊名：JOURNAL OF DIFFERENTIAL EQUATIONS

收录：;EI(收录号：20260235308);Scopus(收录号：2-s2.0-105045867832);WOS:【SCI-EXPANDED(收录号:WOS:001837705600002)】；

基金：The authors are supported by Natural Science Foundation of China (No. 12471045) and Natural Science Foundation of Ningbo (No. 2024J017) .

语种：英文

外文关键词：Finsler manifold; S-curvature; Sobolev space; Caffarelli-Kohn-Nirenberg inequality; Uncertainty principle; Hardy inequality

摘要：In the Riemannian setting, every flat Cartan-Hadamard manifold is isometric to Euclidean space, the canonical model that underlies the theory of Sobolev spaces and guarantees the sharpness/rigidity of the Hardy inequality, the uncertainty principle, and the Caffarelli-Kohn-Nirenberg (CKN) inequality. In this paper, we show that on a flat Finsler Cartan-Hadamard manifold - Berwald's metric space - the classical picture alters radically: the Nash embedding theorem fails, the Sobolev space becomes nonlinear, and the Hardy and uncertainty inequalities break down completely, whereas the CKN inequality exhibits a sharp threshold in its validity depending on a parameter. By contrast, on Funk metric spaces - a class of Finsler Cartan-Hadamard manifolds of constant negative curvature - this threshold behavior disappears, although all the other non-Riemannian features persist. We trace this divergence to the lower bound of the S-curvature. As a consequence, the failure of the aforementioned functional inequalities is established for a broad class of Finsler manifolds that includes both Berwald's and the Funk metric spaces. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.