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arXiv · 1806.02947

Metrics on the Sierpinski carpet by weight functions

Qingsong Gu·Hua Qiu·Huo-Jun Ruan
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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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Qingsong Gu, Hua Qiu, Huo-Jun Ruan. 2018-06-08. Metrics on the Sierpinski carpet by weight functions. https://arxiv.org/abs/1806.02947

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