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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Uniformization of Cantor sets with bounded geometry
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by Vyron Vellis
Conform. Geom. Dyn. 25 (2021), 88-103
Published electronically: August 10, 2021


In this note we provide a quasisymmetric taming of uniformly perfect and uniformly disconnected sets that generalizes a result of MacManus [Rev. Mat. Iberoamericana 15 (1999), pp. 267–277] from 2 to higher dimensions. In particular, we show that a compact subset of $\mathbb {R}^n$ is uniformly perfect and uniformly disconnected if and only if it is ambiently quasiconformal to the standard Cantor set $\mathcal {C}$ in $\mathbb {R}^{n+1}$.
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Bibliographic Information
  • Vyron Vellis
  • Affiliation: Department of Mathematics, The University of Tennessee, Knoxville, Tennessee 37916
  • MR Author ID: 1058764
  • Email:
  • Received by editor(s): January 24, 2021
  • Received by editor(s) in revised form: May 17, 2021
  • Published electronically: August 10, 2021
  • Additional Notes: The author was partially supported by the Academy of Finland project 257482 and NSF DMS grant 1952510.
  • © Copyright 2021 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 25 (2021), 88-103
  • MSC (2020): Primary 30C65; Secondary 30L05
  • DOI:
  • MathSciNet review: 4298216