Poincaré inequality on complete Riemannian manifolds with Ricci curvature bounded below

Original · EN

We prove that complete Riemannian manifolds with polynomial growth and Ricci curvature bounded from below, admit uniform Poincaré inequalities. A global, uniform Poincaré inequality for horospheres in the universal cover of a closed, n-dimensional Riemannian manifold with pinched negative sectional curvature follows as a corollary.