Volume comparison theorems in Finsler spacetimes

Abstract

In a $(1+n)$-dimensional Lorentz--Finsler manifold with $N$-Bakry--Émery Ricci curvature bounded below for $N\in (n,\infty ]$, using the Riccati equation techniques, we established the Bishop--Gromov volume comparison for the so-called standard sets for comparisons in Lorentzian volumes (SCLVs).We also established the Günther volume comparison for SCLVs when the flag curvature was bounded above.

arXiv admin note: text overlap with arXiv:1908.03832

References in corpus (2)

• Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor
• An optimal transport formulation of the Einstein equations of general relativity

Cited by in corpus (1)

• Comparison theorems on weighted Finsler manifolds and spacetimes with $\epsilon$-range