Archive | 2021
Comparison Geometry for Integral Radial Bakry-Émery Ricci Tensor Bounds
Abstract
Abstract. In this paper we prove mean curvature comparisons and volume comparisons on a smooth metric measure space when the integral radial Bakry-Émery Ricci tensor and the potential function or its gradient are bounded. As applications, we prove diameter estimates and eigenvalue estimates on smooth metric measure spaces. These results not only give a supplement of the author’s previous results under integral Bakry-Émery Ricci tensor bounds, but also are generalizations of the Wei-Wylie’s pointwise results.