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

Kombe, Ismail; Özaydin, Murad

doi:10.1090/S0002-9947-2013-05763-7

Hardy-Poincaré, Rellich and uncertainty principle inequalities on Riemannian manifolds
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by Ismail Kombe and Murad Özaydin PDF

Trans. Amer. Math. Soc. 365 (2013), 5035-5050 Request permission

Abstract:

We continue our previous study of improved Hardy, Rellich and uncertainty principle inequalities on a Riemannian manifold $M$, 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 $M$. In particular, we obtain sharp constants for these inequalities on the hyperbolic space $\mathbb {H}^n$.

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