On the Separation Structure of Lalley-Gatzouras Fractals

Published 27 Sep 2019 in math.MG | (1909.12468v1)

Abstract: We obtain a necessary and sufficient condition for Lalley-Gatzouras sets to be uniform disconnected. This enable us to find all Lalley-Gatzouras sets which are quasisymmetrically equivalent to the Cantor ternary set. As another application, we also study the limit behavior of the gap sequence of Lalley-Gatzouras sets.

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