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arXiv · 1912.02055

Ahlfors regular spaces have regular subspaces of any dimension

Nicola Arcozzi·Alessandro Monguzzi·Maura Salvatori
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Abstract

We characterize $Q$-dimensional Ahlfors regular spaces among trees' boundaries and show how to construct, for each $0 < \alpha < Q$, an $\alpha$-regular subspace. As an application, we give an alternative simple proof of the existence of $\alpha$-regular subspaces of a $Q$-dimensional complete Ahlfors regular metric space $(X,\rho)$, which was proved in \cite{JJKRRS}.

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Nicola Arcozzi, Alessandro Monguzzi, Maura Salvatori. 2019-12-04. Ahlfors regular spaces have regular subspaces of any dimension. https://arxiv.org/abs/1912.02055

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