Title: Poincare inequality and Gaussian heat kernel estimate for non-negatively curved graphs

Prof. Lin, Yong, Renmin University, China and Harvard, , 2017-03-07, 3:30-4:30, Hill 005

Abstract: we derive that if a graph has non-negative curvature then it has the volume doubling property, from this we can prove the Gaussian estimate for heat kernel, and then Poincare inequality and Harnack inequality. Under the assumption of positive curvature on graphs, we derive the Bonnet-Myers type theorem that the diameter of graphs is finite and bounded above in terms of the positive curvature. This is a joint work with Horn, Liu and Yau.