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Mathematics > Complex Variables

arXiv:1812.07785 (math)
[Submitted on 19 Dec 2018 (v1), last revised 29 Aug 2019 (this version, v4)]

Title:On the quasiconformal equivalence of dynamical Cantor sets

Authors:Hiroshige Shiga
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Abstract:The complement of a Cantor set in the complex plane is itself regarded as a Riemann surface of infinite type. The problem is the quasiconformal equivalence of such Riemann surfaces. Particularly, we are interested in Riemann surfaces given by Cantor sets which are created through dynamical methods. We discuss the quasiconformal equivalence for the complements of Cantor Julia sets of rational functions and random Cantor sets.
Subjects: Complex Variables (math.CV)
MSC classes: Primary 30C62, Secondary 30F25
Cite as: arXiv:1812.07785 [math.CV]
  (or arXiv:1812.07785v4 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.1812.07785

Submission history

From: Hiroshige Shiga [view email]
[v1] Wed, 19 Dec 2018 07:21:05 UTC (194 KB)
[v2] Thu, 20 Dec 2018 16:23:12 UTC (194 KB)
[v3] Fri, 21 Dec 2018 08:52:22 UTC (194 KB)
[v4] Thu, 29 Aug 2019 07:00:39 UTC (123 KB)
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