Ricci Tensor for Diffusion Operators and Curvature-Dimension Inequalities under Conformal Transformations and Time Changes
Metric Geometry
2017-08-09 v3
Abstract
Within the -calculus of Bakry and Ledoux, we define the Ricci tensor induced by a diffusion operator, we deduce precise formulas for its behavior under drift transformation, time change and conformal transformation, and we derive new transformation results for the curvature-dimension conditions of Bakry-Emery as well as for those of Lott-Sturm-Villani. Our results are based on new identities and sharp estimates for the -Ricci tensor and for the Hessian. In particular, we obtain Bochner's formula in the general setting.
Cite
@article{arxiv.1401.0687,
title = {Ricci Tensor for Diffusion Operators and Curvature-Dimension Inequalities under Conformal Transformations and Time Changes},
author = {Karl-Theodor Sturm},
journal= {arXiv preprint arXiv:1401.0687},
year = {2017}
}
Comments
Minor corrections