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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.


Quadrature domains and the real quadratic family
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by Kirill Lazebnik
Conform. Geom. Dyn. 25 (2021), 104-125
Published electronically: September 15, 2021


We study several classes of holomorphic dynamical systems associated with quadrature domains. Our main result is that real-symmetric polynomials in the principal hyperbolic component of the Mandelbrot set can be conformally mated with a congruence subgroup of $\mathrm {PSL}(2,\mathbb {Z})$, and that this conformal mating is the Schwarz function of a simply connected quadrature domain.
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Bibliographic Information
  • Kirill Lazebnik
  • Affiliation: Department of Computer and Mathematical Sciences, University of Toronto, Toronto, Canada
  • MR Author ID: 1006341
  • ORCID: 0000-0001-8963-4410
  • Email:
  • Received by editor(s): October 19, 2020
  • Received by editor(s) in revised form: April 8, 2021, and June 16, 2021
  • Published electronically: September 15, 2021
  • © Copyright 2021 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 25 (2021), 104-125
  • MSC (2020): Primary 30C10; Secondary 37F10
  • DOI:
  • MathSciNet review: 4312998