@article{da5810b751054ebcb922f122eb248da1,
title = "Poincar{\'e} 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 Poincar{\'e} inequalities. A global, uniform Poincar{\'e} inequality for horospheres in the universal cover of a closed, n-dimensional Riemannian manifold with pinched negative sectional curvature follows as a corollary.",
author = "G{\'e}rard Besson and Gilles Courtois and Sa'ar Hersonsky",
note = "Funding Information: Acknowledgement. The research in this paper greatly benefited from visits of the authors at Institut Fourier, IHP, Paris VI, Princeton University and the University of Georgia. The authors express their gratitude for their hospitality. We would also like to deeply thank Tobias Colding and Laurent Saloff-Coste for their advice and insight regarding the subject of this paper. G. Besson is supported by ERC Advanced Grant 320939, GETOM. S. Hersonsky is supported by grant 319163 from the Simons Foundation. Publisher Copyright: {\textcopyright} 2018 International Press of Boston, Inc.. All rights reserved.",
year = "2018",
month = jan,
day = "1",
doi = "10.4310/MRL.2018.v25.n6.a3",
language = "English",
volume = "25",
pages = "1741--1769",
journal = "Mathematical Research Letters",
issn = "1073-2780",
publisher = "International Press of Boston, Inc.",
number = "6",
}