Curvature-dimension conditions for diffusions under time change

2019/07/12 by Bang-Xian Han, Han, Bang-Xian, Karl‐Theodor Sturm +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1907.05761

openalex publication_date 2019/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive precise transformation formulas for synthetic lower Ricci bounds under time change. More precisely, for local Dirichlet forms we study how the curvature-dimension condition in the sense of Bakry-Emery will transform under time change. Similarly, for metric measure spaces we study how the curvature-dimension condition in the sense of Lott-Sturm-Villani will transform under time change.

Citations

• Ricci curvature for metric-measure spaces via optimal transport
• On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces
• Metric measure spaces with Riemannian Ricci curvature bounded from below

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• Self-improvement of the Bakry-Emery criterion for Poincaré inequalities and Wasserstein contraction using variable curvature bounds
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