Metrics on the Sierpinski carpet by weight functions

2018/06/08 by Gu, Qingsong, Qiu, Hua, Ruan, Huo-Jun
#28A80 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1806.02947

Abstract

We construct certain metrics on the Sierpinski carpet via a class of self-similar weight functions. Using these metrics and by applying known results, we obtain the two-sided sub-Gaussian heat kernel estimates of time change of the standard diffusion on the Sierpinski carpet with respect to self-similar measures. This proves a conjecture by Kigami.

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