Guofang Wei, UC Santa Barbara

Title: Relative volume comparison for integral Ricci curvature and some applications.

Abstract: We give several Bishop-Gromov relative volume comparisons in terms of integral Ricci curvature which improve the results in Petersen-Wei. Using one of these volume comparisons, we derive an optimal volume entropy estimate for integral Ricci curvature bound. We also obtain an almost minimal volume rigidity for integral Ricci curvature. This is a joint work with Lina Chen.