Hardy-Poincaré, Rellich and uncertainty principle inequalities on Riemannian manifolds

Abstract

We continue our previous study of improved Hardy, Rellich and uncertainty principle inequalities on a Riemannian manifold M M , started in our earlier paper from 2009. In the present paper we prove new weighted Hardy-Poincaré, Rellich type inequalities as well as an improved version of our uncertainty principle inequalities on a Riemannian manifold M M . In particular, we obtain sharp constants for these inequalities on the hyperbolic space H n \mathbb {H}^n .