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

Published 29 Oct 2025 in math.MG and math.GN | (2510.25076v1)

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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