Speaker: Prof. Qi Guo (Renmin University of China)

Title: Volume Doubling and Poincaré inequalities for bounded-degree graphs with nonnegative Bakry-Émery curvature condition

Time: 16:00-17:00 September 17, 2026 (Thursday)

Inviter: Prof. Jinpin Zhuge (MCM)

Place: MCM110

Abstract: In this talk, we will show the proof of volume doubling, polynomial growth and a scale-invariant Poincaré inequality on bounded-degree graphs with nonnegative Bakry–Émery curvature. We use Münch's modified nonlinear heat flow, extended to infinite graphs by Pajot and Russ and the heat-kernel estimates. The key novelty lies in a unified local estimate for the Laplacians of both the linear and nonlinear heat flows, which is then combined with a resolvent argument and semigroup interpolation in the linear setting, and with the maximum principle in the nonlinear setting. This is a joint work with Xueping Huang and Yi C. Huang.