Quantitative Rellich Inequalities on Finsler-Hadamard Manifolds

Kristály, Alexandru and Repovš, Dušan (2016) Quantitative Rellich Inequalities on Finsler-Hadamard Manifolds. Communications in Contemporary Mathematics, 18 (6). pp. 1-17. ISSN 0219-1997, ESSN: 1793-6683

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Abstract

In this paper, we are dealing with quantitative Rellich inequalities on Finsler–Hadamard manifolds where the remainder terms are expressed by means of the flag curvature. By exploring various arguments from Finsler geometry and PDEs on manifolds, we show that more weighty curvature implies more powerful improvements in Rellich inequalities. The sharpness of the involved constants is also studied. Our results complement those of Yang, Su and Kong [Hardy inequalities on Riemannian manifolds with negative curvature, Commun. Contemp. Math. 16 (2014), Article ID: 1350043, 24 pp.].

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