Structure of spaces with Bakry-\'Emery Ricci curvature bounded below
Abstract
In this paper, we explore the limit structure of a sequence of Riemannian manifolds with Bakry-\'Emery Ricci curvature bounded below in the Gromov-Hausdorff topology. By extending the techniques established by Cheeger-Cloding for Riemannian manifolds with Ricci curvature bounded below, we prove that each tangent space at a point of the limit space is a metric cone. We also analyze the singular structure of the limit space analogous to a work of Cheeger-Colding-Tian. Our results will be applied to study the limit space of a sequence of K\"ahler metrics arising from solutions of certain complex Monge-Amp\`ere equations for the existence of K\"ahler-Ricci solitons on a Fano manifold via the continuity method.
Keywords
Cite
@article{arxiv.1304.4490,
title = {Structure of spaces with Bakry-\'Emery Ricci curvature bounded below},
author = {Feng Wang and Xiaohua Zhu},
journal= {arXiv preprint arXiv:1304.4490},
year = {2016}
}
Comments
The proof of Theorem 5.4 is modified. Some typos are corrected