Poincare inequality on complete Riemannian manifolds with Ricci curvature bounded below

Gérard Besson (1) , Gilles Courtois (2) , Sa'Ar Hersonsky (3)

1 IF - Institut Fourier
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
3 University of Georgia [USA]

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.

Domaines: Géométrie différentielle [math.DG]

Gérard Besson, Gilles Courtois, Sa'Ar Hersonsky. Poincare inequality on complete Riemannian manifolds with Ricci curvature bounded below. 2018. ⟨hal-01685128⟩