Riemannian and Lorentzian volume comparisons with the Bakry-Emery Ricci tensor

The Bishop and Bishop-Gromov volume comparisons with the Bakry-Emery Ricci tensor in a metric measure space are studied by the comparisons of the Jacobi differential equations in a Riemannian and Lorentzian manifold.

1. Introduction

2. Preliminaries

3. Riemannian volume comparisons with the Bakry-Emery Ricci tensor

4. Lorentzian volume comparisons with the Bakry-Emery Ricci tensor

References

(0)

(0)

(0)

(0)