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

By I. Kombe, M. Ozaydin. 2011

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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-Poincar\'e, 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 $\mathbb{H}^n$.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/424c5f8e361fd5b7453c099bafc0b20bb73d7623