Sharp Geometric and Functional Inequalities in Metric Measure Spaces with Lower Ricci Curvature Bounds

Abstract

Abstract. For metric measure spaces verifying the reduced curvature-dimension condition CD∗(K,N) we prove a series of sharp functional inequalities under the additional assumption of essentially nonbranching. Examples of spaces entering this framework are (weighted) Riemannian manifolds satisfying lower Ricci curvature bounds and their measured Gromov… (More)

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