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On the conformal walk dimension: Quasisymmetric uniformization for symmetric diffusions
[article]
2022
arXiv
pre-print
We introduce the notion of conformal walk dimension, which serves as a bridge between elliptic and parabolic Harnack inequalities. The importance of this notion is due to the fact that, for a given strongly local, regular symmetric Dirichlet space in which every metric ball has compact closure (MMD space), the finiteness of the conformal walk dimension characterizes the conjunction of the metric doubling property and the elliptic Harnack inequality. Roughly speaking, the conformal walk
arXiv:2008.12836v4
fatcat:yg57dyomk5gmlfgic3axv3p3zi