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.


Mappings of finite distortion: Formation of cusps II
HTML articles powered by AMS MathViewer

by Juhani Takkinen
Conform. Geom. Dyn. 11 (2007), 207-218
Published electronically: October 18, 2007


For $s>0$ given, we consider a planar domain $\Omega _s$ with a rectifiable boundary but containing a cusp of degree $s$, and show that there is no homeomorphism $f\colon \mathbb {R}^2\to \mathbb {R}^2$ of finite distortion with $\exp (\lambda K)\in L^1_{\mathrm {loc}}(\mathbb {R}^2)$ so that $f(B)=\Omega _s$ when $\lambda >4/s$ and $B$ is the unit disc. On the other hand, for $\lambda <2/s$ such an $f$ exists. The critical value for $\lambda$ remains open.
Similar Articles
  • Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2000): 30C62, 30C65
  • Retrieve articles in all journals with MSC (2000): 30C62, 30C65
Bibliographic Information
  • Juhani Takkinen
  • Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FI-40014 Finland
  • Email:
  • Received by editor(s): May 21, 2007
  • Published electronically: October 18, 2007
  • Additional Notes: The author was partially supported by the foundation Vilho, Yrjö ja Kalle Väisälän rahasto.
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 11 (2007), 207-218
  • MSC (2000): Primary 30C62, 30C65
  • DOI:
  • MathSciNet review: 2354095