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In this paper we obtain Hardy, weighted Trudinger-Moser andCaffarelli-Kohn-Nirenberg type inequalities with sharp constants on Riemannianmanifolds with non-positive sectional curvature and, in particular, a varietyof new estimates on hyperbolic spaces. Moreover, in some cases we also showtheir equivalence with Trudinger-Moser inequalities. As consequences, therelations between the constants of these inequalities are investigated yieldingasymptotically best constants in the obtained inequalities. We also obtain thecorresponding uncertainty type principles.

Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds with negative curvature