Every Lipschitz metric has $C^1$-geodesics

Abstract

We prove that the geodesic equation for any semi-Riemannian metric of regularity $C^{0,1}$ possesses $C^1$-solutions in the sense of Filippov.

final version, minor corrections

References in corpus (5)

• Convex neighborhoods for Lipschitz connections and sprays
• Length structures on manifolds with continuous Riemannian metrics
• The exponential map of a $C^{1,1}$-metric
• The regularity of geodesics in impulsive pp-waves
• Generalized regularity and solution concepts for differential equations

Cited by in corpus (14)

• Causality theory for closed cone structures with applications
• Singularity theorems for $C^1$-Lorentzian metrics
• The singularity theorems of General Relativity and their low regularity extensions
• The global uniqueness and $C^1$-regularity of geodesics in expanding impulsive gravitational waves
• Memory Effect and BMS-like Symmetries for Impulsive Gravitational Waves
• The global existence, uniqueness and C^1-regularity of geodesics in nonexpanding impulsive gravitational waves
• On geodesics in low regularity
• Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, Part I
• Cut-and-paste for impulsive gravitational waves with $\Lambda$: The geometric picture
• Penrose junction conditions with $\Lambda$: Geometric insights into low-regularity metrics for impulsive gravitational waves
• The memory effect in impulsive plane waves: comments, corrections, clarifications
• Penrose junction conditions extended: impulsive waves with gyratons
• Spacetime singularities and curvature blow-ups
• Cut-and-paste for impulsive gravitational waves with $\Lambda$: The mathematical analysis