10 citations · 23 across the 6 of their papers we have counts for
20 papers
Weak curvature conditions and functional inequalities
John Lott, Cedric Villani
We give sufficient conditions for a measured length space (X,d,m) to admit local and global Poincare inequalities. We first introduce a condition DM on (X,d,m), defined in terms of…
Remark about scalar curvature and Riemannian submersions
John Lott
We consider modified scalar curvature functions for Riemannian manifolds equipped with smooth measures. Given a Riemannian submersion whose fiber transport is measure-preserving up…
Ricci curvature for metric-measure spaces via optimal transport
John Lott, Cedric Villani
We define a notion of a measured length space X having nonnegative N-Ricci curvature, for N finite, or having infinity-Ricci curvature bounded below by K, for K a real number. The…
Local index theory over foliation groupoids
Alexander Gorokhovsky, John Lott
We give a superconnection proof of an index theorem for a Dirac-type operator that is invariant with respect to the action of a foliation groupoid.
Limit sets as examples in noncommutative geometry
John Lott
The fundamental group of a hyperbolic manifold acts on the limit set, giving rise to a cross-product C^* algebra. We construct nontrivial K-cycles for the cross-product algebra, th…
Some Geometric Properties of the Bakry-Emery-Ricci Tensor
John Lott
The Bakry-Emery tensor gives an analog of the Ricci tensor for a Riemannian manifold with a smooth measure. We show that some of the topological consequences of having a positive o…