Good geodesics satisfying the timelike curvature-dimension condition

DOI10.1016/j.na.2022.113205OpenAlexW4313442773MaRDI QIDQ2688998

Mathias Braun

Publication date: 6 March 2023

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.06950

zbMATH Keywords

timelike geodesicsstrong energy conditionLorentzian pre-length spacestimelike curvature-dimension condition

Mathematics Subject Classification ID

Applications of global analysis to the sciences (58Z05) General relativity (83C99) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (3)

Further observations on the definition of global hyperbolicity under low regularity ⋮ Rényi's entropy on Lorentzian spaces. Timelike curvature-dimension conditions ⋮ A synthetic null energy condition

Cites Work

• Unnamed Item
• Improved geodesics for the reduced curvature-dimension condition in branching metric spaces
• Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm
• Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
• Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below
• On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
• Localization and tensorization properties of the curvature-dimension condition for metric measure spaces
• A Riemannian interpolation inequality à la Borell, Brascamp and Lieb
• On quotients of spaces with Ricci curvature bounded below
• Super-Ricci flows for metric measure spaces
• Lorentzian length spaces
• Displacement convexity of Boltzmann's entropy characterizes the strong energy condition from general relativity
• The globalization theorem for the curvature-dimension condition
• On the existence of dual solutions for Lorentzian cost functions
• Ricci curvature for metric-measure spaces via optimal transport
• Causality for nonlocal phenomena
• Structure theory of metric measure spaces with lower Ricci curvature bounds
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• Null distance on a spacetime
• On the differential structure of metric measure spaces and applications
• Transport inequalities, gradient estimates, entropy and Ricci curvature
• The singularities of gravitational collapse and cosmology
• Theory of optimal transport for Lorentzian cost functions
• Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows
• Causality theory for closed cone structures with applications
• Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces
• Riemannian Ricci curvature lower bounds in metric measure spaces with 𝜎-finite measure
• Gravitational Collapse and Space-Time Singularities
• Optimal maps in essentially non-branching spaces
• The occurrence of singularities in cosmology
• Domain of Dependence
• The Large Scale Structure of Space-Time
• Optimal Transport
• Polar factorization of maps on Riemannian manifolds
• Rényi's entropy on Lorentzian spaces. Timelike curvature-dimension conditions

This page was built for publication: Good geodesics satisfying the timelike curvature-dimension condition