2025/10/29 by Zhang, Yanfang, Zhang, Shu-Qin
#26A16 #28A12 #28A80 #FOS: Mathematics #General Topology (math.GN) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2510.25076
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.