Comparison Theorems on Weighted Finsler Manifolds and Spacetimes with ε-Range

We establish the Bonnet-Myers theorem, Laplacian comparison theorem, and Bishop-Gromov volume comparison theorem for weighted Finsler manifolds as well as weighted Finsler spacetimes, of weighted Ricci curvature bounded below by using the weight function. These comparison theorems are formulated with epsilon-range introduced in our previous paper, that provides a natural viewpoint of interpolating weighted Ricci curvature conditions of different effective dimensions. Some of our results are new even for weighted Riemannian manifolds and generalize comparison theorems of Wylie-Yeroshkin and Kuwae-Li.

Automated summary

In this study, we establish the Bonnet-Myers theorem, Laplacian comparison theorem, and Bishop-Gromov volume comparison theorem for weighted Finsler manifolds and weighted Finsler spacetimes with weighted Ricci curvature bounded below using the weight function. These comparison theorems are formulated with the introduction of epsilon-range, providing a natural viewpoint for interpolating weighted Ricci curvature conditions of different effective dimensions. Some of our results are new even for weighted Riemannian manifolds and generalize the comparison theorems of Wylie-Yeroshkin and Kuwae-Li.