HAL (Le Centre pour la Communication Scientifique Directe) · 2012 · 373 citations · 30 references
Natural SciencesPhysicsHeat TransferThermodynamicsBoundary ConditionsContinuity EquationHeat FlowMetric GeometryRiemannian GeometryCompactness TheoremsCurvature Bounded AboveCurvature Bounded BelowMetric Measure SpacesRicci CurvatureRicci FlowRicci Tensor
Minor typos corrected and many small improvements added. Lemma 2.4, Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop. 4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6 simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients, still equivalent to all other ones, has been proposed
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Ricci curvature for metric-measure spaces via optimal transport
John Lott, Cédric Villani · Annals of Mathematics · 2009 · 1.3K citations · Full text
On the geometry of metric measure spaces. II
Karl‐Theodor Sturm · Acta Mathematica · 2006 · 1.3K citations · Full text