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(Jun. 14) Long time behavior of discrete Ollivier Ricci flow

Last updated :2019-06-10

Topic: Long time behavior of discrete Ollivier Ricci flow
Speaker: Dr. Florentin Münch
(Max Planck Institute for Mathematics in the Sciences)
Time: 16:00-17:00, Friday, June 14, 2019
Venue: Room 416, Mathematics Building, Guangzhou South Campus, SYSU

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.