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 $M$, started in \cite{Kombe-Ozaydin}. In the present paper we prove new weighted Hardy-Poincaré, Rellich type inequalities as well as improved version of our Uncertainty principle inequalities on a Riemannian manifold $M$. In particular, we obtain sharp constants for these inequalities on the hyperbolic space ${\mathbb{H}}^n$.

References in corpus (1)

• On the best possible remaining term in the Hardy Inequality

Cited by in corpus (1)

• Poincaré and Hardy inequalities on homogeneous trees