2013/08/19 by Qiaohua Yang, QIAOHUA YANG, Dan Su +3 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Arithmetic #Curvature #Euclidean geometry #Geodesic #Geometric Analysis and Curvature Flows #Geometry #Inequality #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Pure mathematics #Remainder #Ricci curvature #Ricci-flat manifold #Riemannian manifold #Scalar curvature #Sectional curvature
paper · doi:10.1142/s0219199713500430
openalex publication_date 2013/08/19 · crossref created 2013/08/19 · crossref issued 2014/04/01 · crossref published 2014/04/01 · crossref published-print 2014/04/01 · crossref published-online 2014/04/21 · crossref deposited 2020/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11 · crossref indexed 2026/07/31
Let M be a complete, simply connected Riemannian manifold with negative curvature. We obtain the sharp constants of Hardy and Rellich inequalities related to the geodesic distance on M. Furthermore, if M is with strictly negative curvature, we show that the L p Hardy inequalities can be globally refined by adding remainder terms like the Brezis–Vázquez improvement in case p ≥ 2, which is contrary to the case of Euclidean spaces.