arXiv (Cornell University) · 2010 · 115 citations · 9 references
Natural SciencesMathematicsGeometryCurvature AnalysisDifferential GeometryMetric GeometryRiemannian GeometryCross-sectional CurvatureCurvatureCurvature Bounded AboveCurvature Bounded BelowRicci CurvatureRicci TensorSectional Curvature Measures
Here I show compatibility of two definition of generalized curvature bounds --- the lower bound for sectional curvature in the sense of Alexandrov and lower bound for Ricci curvature in the sense of Lott--Villani--Sturm.
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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
A Convexity Principle for Interacting Gases
Robert J. McCann · Advances in Mathematics · 1997 · 923 citations