Metrics on the Sierpinski carpet by weight functions
Functional Analysis
2018-06-15 v2
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.
Keywords
Cite
@article{arxiv.1806.02947,
title = {Metrics on the Sierpinski carpet by weight functions},
author = {Qingsong Gu and Hua Qiu and Huo-Jun Ruan},
journal= {arXiv preprint arXiv:1806.02947},
year = {2018}
}
Comments
21 pages, 4 figures