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Conformal Geometry and Dynamics

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A note to ``Mappings of finite distortion: formation of cusps II''

Authors: Pekka Koskela and Juhani Takkinen
Journal: Conform. Geom. Dyn. 14 (2010), 184-189
MSC (2010): Primary 30C62, 30C65
Published electronically: July 15, 2010
MathSciNet review: 2670509
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Abstract: We consider planar homeomorphisms $ f\colon\mathbb{R}^2\to\mathbb{R}^2$ that are of finite distortion and map the unit disk onto a specific cusp domain $ \Omega_s$. We study the relation between the degree $ s$ of the cusp and the integrability of the distortion function $ K_f$ by sharpening a previous result where $ K_f$ is assumed to be locally exponentially integrable.

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Additional Information

Pekka Koskela
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FI-40014 University of Jyväskylä, Finland

Juhani Takkinen
Affiliation: Linnantie 8 C 21, 40800 Vaajakoski, Finland

Keywords: Cusp, homeomorphism, mapping of finite distortion
Received by editor(s): April 17, 2010
Published electronically: July 15, 2010
Additional Notes: The first author was partially supported by the Academy of Finland grants nos. 120927 and 131477
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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