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arXiv · 2510.25076

When the conformal dimension of a self-affine sponge of Lalley-Gatzouras type is zero

Yanfang Zhang·Shu-Qin Zhang
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Abstract

It is well known that if a metric space is uniformly disconnected, then its conformal dimension is zero. First, we characterize when a self-affine sponge of Lalley-Gatzouras type is uniformly disconnected. Thanks to this characterization, we show that a self-affine sponge of Lalley-Gatzouras type has conformal dimension zero if and only if it is uniformly disconnected.

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Yanfang Zhang, Shu-Qin Zhang. 2025-10-29. When the conformal dimension of a self-affine sponge of Lalley-Gatzouras type is zero. https://arxiv.org/abs/2510.25076

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