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math.DG2005★ 2 cited
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…
math.DG2004★ 10 cited
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…