Skip to Main Content

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.


Geometric construction of quasiconformal mappings in the Heisenberg group
HTML articles powered by AMS MathViewer

by Robin Timsit
Conform. Geom. Dyn. 22 (2018), 99-140
Published electronically: August 22, 2018


In this paper, we are interested in the construction of quasiconformal mappings between domains of the Heisenberg group $\mathbf {H}$ that minimize a mean distortion functional. We propose to construct such mappings by considering a corresponding problem between domains of Poincaré half-plane $\mathbb H$ and then, lifting every of its solutions to $\mathbf H$. The first map we construct is a quasiconformal map between two cylinders. We explain the method used to find it and prove its uniqueness up to rotations. Then, we give geometric conditions which ensure that a minimizer (in $\mathbf {H}$) comes as a lift of a minimizer between domains of $\mathbb H$. Finally, as a non-trivial example of the generalization, we manage to reconstruct the map from [Ann. Acad. Sci. Fenn. Math. 38 (2013), pp. 149–180] between two spherical annuli and prove its uniqueness as a minimizer.
Similar Articles
  • Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2010): 30L10, 30C75
  • Retrieve articles in all journals with MSC (2010): 30L10, 30C75
Bibliographic Information
  • Robin Timsit
  • Affiliation: Sorbonne Université, Université Paris Diderot, CNRS, Institut de Mathématiques de Jussieu-Paris Rive Gauche, IMJ-PRG, F-75005, Paris, France
  • Email:
  • Received by editor(s): December 6, 2016
  • Received by editor(s) in revised form: May 29, 2017, and March 23, 2018
  • Published electronically: August 22, 2018
  • © Copyright 2018 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 22 (2018), 99-140
  • MSC (2010): Primary 30L10, 30C75
  • DOI:
  • MathSciNet review: 3845546