Mathematical Research Letters

Volume 25 (2018)

Number 6

Poincaré inequality on complete Riemannian manifolds with Ricci curvature bounded below

Pages: 1741 – 1769



Gérard Besson (Institut Fourier, Université Grenoble Alpes, Gières, France)

Gilles Courtois (UPMC, Sorbonne Université, Institut de Mathématiques de Jussieu, Paris, France)

Sa’ar Hersonsky (Department of Mathematics, University of Georgia, Athens, Ga., U.S.A.)


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.

Received 13 January 2018

Accepted 29 August 2018

Published 25 March 2019