A Sierpinski carpet like fractal without standard self-similar energy

Cao, Shiping; Qiu, Hua

doi:10.1090/proc/16146

A Sierpinski carpet like fractal without standard self-similar energy
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by Shiping Cao and Hua Qiu;

Proc. Amer. Math. Soc. 151 (2023), 1087-1102

DOI: https://doi.org/10.1090/proc/16146

Published electronically: December 21, 2022

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Abstract:

We construct a Sierpinski carpet like fractal, on which a diffusion with sub-Gaussian heat kernel estimate does not exist, in contrast to previous researches on the existence of such diffusions, on the generalized Sierpinski carpets and recently introduced unconstrained Sierpinski carpets.

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