Speaker: Pro.Huojun Ruan（Zhejiang University）

Title: Metrics on fractals by symmetric self-similar weight functions

Time: Sun, Apr.28, 2019, PM:16:30-17:30

Location: Room 4224, Building No.4, Wushan Campus

Abstract:

       I will talk about the method (proposed by Kigami) of defining metrics on two classes of fractals (nested fractals and generalized Sierpinski carpets) by using symmetric self-similar weight functions on its symbolic spaces. We proved that there is a critical surface for the weights to give a geodesic metric. These metrics are crucial in describing heat kernel bounds for time-change Brownian motions on these fractals via symmetric self-similar measures. We also compute the critical surface for two examples, one is the Lindstrom snowflake and the other is the standard Sierpinski carpet. This is based on a joint work with Qingsong Gu, Ka-Sing Lau and Hua Qiu.