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Deformations on symbolic Cantor sets and ultrametric spaces

Published 4 Nov 2019 in math.CV and math.MG | (1911.01017v1)

Abstract: By introducing new deformations on symbolic Cantor sets and ultrametric spaces, we prove that doubling ultrametric spaces admit bilipschitz embedding into Cantor sets. If in addition the spaces are uniformly perfect, we show that they are quasisymmetrically equivalent to Cantor sets. As an application, we provide a new proof for a recent work of Heer (Anal. Geom. Metr. Spaces, 2017) regarding quasim\"obius uniformization of Cantor set.

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