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HARDY INEQUALITIES ON RIEMANNIAN MANIFOLDS WITH NEGATIVE CURVATURE

QIAOHUA YANG

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China

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DAN SU

School of Statistics, University of International Business and Economics, Beijing 100029, P. R. China

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, and

YINYING KONG

School of Mathematics and Statistics, Guangdong University of Business Studies, Guangzhou 510320, P. R. China

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https://doi.org/10.1142/S0219199713500430Cited by:34 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 26D10, 46E35

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