Quantitative Rellich Inequalities on Finsler-Hadamard Manifolds

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 are also studied. Our results complement those of Yang, Su and Kong [Commun. Contemp. Math., 2014].

14 pages. To appear in Communications in Contemporary Mathematics

References in corpus (1)

• Singular Poisson equations on Finsler-Hadamard manifolds

Cited by in corpus (4)

• Hardy-Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs
• Hardy type inequalities on closed manifolds via Ricci curvature
• Rellich inequalities via Riccati pairs on model space forms
• A bipolar Hardy inequality on Finsler manifolds