On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces

2014/12/19 by Matthias Erbar, Kazumasa Kuwada, Karl-Theodor Sturm · 38 citations
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research

paper · doi:10.1007/s00222-014-0563-7

Citations

• Ricci curvature for metric-measure spaces via optimal transport
• On the parabolic kernel of the Schrödinger operator

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• Semiconvexity of (weak) Kantorovich potentials in the Lorentzian optimal transport problem
• Weak curvature conditions on metric graphs
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• Harmonic functions with polynomial growth on manifolds with nonnegative Ricci curvature
• Stability in Gagliardo-Nirenberg-Sobolev inequalities: flows, regularity and the entropy method
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• Space-time Wasserstein controls and Bakry-Ledoux type gradient estimates
• Lower Bound Estimates for The First Eigenvalue of The Weighted p-Laplacian on Smooth Metric Measure Spaces
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• Harmonic functions on metric measure spaces
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• Characterizations of Bounded Ricci Curvature on Smooth and NonSmooth Spaces
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• W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds
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• A Noncommutative Transport Metric and Symmetric Quantum Markov Semigroups as Gradient Flows of the Entropy
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• On the asymptotic behavior of the dimension of spaces of harmonic functions with polynomial growth
• Sharp Cheeger-Buser Type Inequalities in RCD ( K , ∞ ) Spaces. [europepmc]
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• On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth. [europepmc]
• Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups. [europepmc]
• Moduli spaces of compact RCD(0,N)-structures. [europepmc]
• Ricci curvature bounds and rigidity for non-smooth Riemannian and semi-Riemannian metrics. [europepmc]