Poincaré inequality on complete Riemannian manifolds with Ricci curvature bounded below

Abstract

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.

arXiv comment20 pages, 2 fugures