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arXiv · 1803.11296

Quasisymmetric uniformization and heat kernel estimates

Mathav Murugan
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Abstract

We show that the circle packing embedding in $\mathbb{R}^2$ of a one-ended, planar triangulation with polynomial growth is quasisymmetric if and only if the simple random walk on the graph satisfies sub-Gaussian heat kernel estimate with spectral dimension two. Our main results provide a new family of graphs and fractals that satisfy sub-Gaussian estimates and Harnack inequalities.

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Mathav Murugan. 2018-03-30. Quasisymmetric uniformization and heat kernel estimates. https://arxiv.org/abs/1803.11296

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