Contents Online
Mathematical Research Letters
Volume 25 (2018)
Number 6
Poincaré inequality on complete Riemannian manifolds with Ricci curvature bounded below
Pages: 1741 – 1769
DOI: https://dx.doi.org/10.4310/MRL.2018.v25.n6.a3
Authors
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.
Received 13 January 2018
Accepted 29 August 2018
Published 25 March 2019