Improved Hardy and Rellich inequalities on nonreversible Finsler manifolds

In this paper, we study the sharp constants of quantitative Hardy and Rellich inequalities on nonreversible Finsler manifolds equipped with arbitrary measures. In particular, these inequalities can be globally refined by adding remainder terms like the Brezis-V\'azquez improvement, if Finsler manifolds are of strictly negative flag curvature, vanishing S-curvature and finite uniformity constant. Furthermore, these results remain valid when Finsler metrics are reversible.