Good geodesics satisfying the timelike curvature-dimension condition

2022/05/14 by Mathias Braun, Braun, Mathias · 1 citation
Mathematics · #49J52 #53C50 #58E10 #58Z05 #83C99 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2205.06950

openalex publication_date 2022/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (M,d,\mathfrakm,≪,≤,τ) be a causally closed, \mathscrK-globally hyperbolic, regular measured Lorentzian geodesic space satisfying the weak timelike curvature-dimension condition \smashwTCD_p^e(K,N) in the sense of Cavalletti and Mondino. We prove the existence of geodesics of probability measures on M which satisfy the entropic semiconvexity inequality defining \smashwTCD_p^e(K,N) and whose densities with respect to \mathfrakm are additionally uniformly L^∞ in time. This holds apart from any nonbranching assumption. We also discuss similar results under the timelike measure-contraction property.

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• Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group

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