Title：Long time behavior of discrete Ollivier Ricci flow

Speaker：Florentin Münch  （Max Planck Institute）

Time：2019年6月29日      上午  09:30-10:30

Room：东区管理科研楼   0029cc金沙贵宾会1308室

Abstract：We first give an introduction on discrete Ricci curvature based on gradient estimates of the heat semigroup. We then give an overview of analytic and geometric consequences of lower Ricci curvature bounds. Following David Gu et al., we introduce the discrete Ricci flow based on Ollivier Ricci curvature. We show long time convergence of the normalized metric under the discrete Ricci flow. Moreover, we discuss several monotonicity properties of the flow and give examples for slow convergence speed. We first give an introduction on discrete Ricci curvature based on gradient estimates of the heat semigroup. We then give an overview of analytic and geometric consequences of lower Ricci curvature bounds. Following David Gu et al., we introduce the discrete Ricci flow based on Ollivier Ricci curvature. We show long time convergence of the normalized metric under the discrete Ricci flow. Moreover, we discuss several monotonicity properties of the flow and give examples for slow convergence speed.