A Sierpinski carpet like fractal without standard self-similar energy

Shiping Cao; Hua Qiu

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arXiv · 2109.12760

A Sierpinski carpet like fractal without standard self-similar energy

Shiping Cao·Hua Qiu

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Abstract

We construct a Sierpinski carpet like fractal, on which a self-similar 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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Shiping Cao, Hua Qiu. 2021-09-27. A Sierpinski carpet like fractal without standard self-similar energy. https://arxiv.org/abs/2109.12760

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