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].