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A sharp uncertainty principle and Hardy-Poincaré inequalities on sub-Riemannian manifolds
We prove a sharp Heisenberg uncertainty principle inequality and Hardy-Poincaré inequality on the sub-Riemannian manifold R 2n+1 = R n × R n × R defined by the vector fields:where |z| = (|x| 2 + |y| 2 ) 1/2 and k 1 .