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A note to ``Mappings of finite distortion: formation of cusps II''
Author(s):
Pekka
Koskela;
Juhani
Takkinen
Journal:
Conform. Geom. Dyn.
14
(2010),
184-189.
MSC (2010):
Primary 30C62, 30C65
Posted:
July 15, 2010
MathSciNet review:
2670509
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Abstract:
We consider planar homeomorphisms  that are of finite distortion and map the unit disk onto a specific cusp domain  . We study the relation between the degree  of the cusp and the integrability of the distortion function  by sharpening a previous result where  is assumed to be locally exponentially integrable.
References:
-
- 1.
- L.V. Ahlfors, Quasiconformal reflections, Acta Math. 109 (1963), 291-301. MR 0154978 (27:4921)
- 2.
- P. Haïssinsky, Chirurgie parabolique, C. R. Acad. Sci. Paris Sér. I Math. 327 (1998), no. 2, 195-198. MR 1645124 (99i:58127)
- 3.
- P. Koskela and J. Onninen, Mappings of finite distortion: Capacity and modulus inequalities, J. Reine Angew. Math. 599 (2006), 1-26. MR 2279096 (2007k:30035)
- 4.
- P. Koskela and J. Takkinen, Mappings of finite distortion: formation of cusps, Publ. Mat. 51 (2007), no. 1, 223-242. MR 2307153 (2008e:30026)
- 5.
- -, Mappings of finite distortion: Formation of cusps III, Acta. Math. Sin. (English Series) 26 (2010), no. 5, 817-824.
- 6.
- O. Lehto and K.I. Virtanen, Quasiconformal mappings in the plane, second ed., Springer-Verlag, New York, 1973. MR 0344463 (49:9202)
- 7.
- J. Onninen and X. Zhong, A note on mappings of finite distortion: the sharp modulus of continuity, Michigan Math. J. 53 (2005), no. 2, 329-335. MR 2152704 (2006c:30025)
- 8.
- Ch. Pommerenke, Boundary behaviour of conformal maps, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 299, Springer-Verlag, Berlin, 1992. MR 1217706 (95b:30008)
- 9.
- J. Takkinen, Mappings of finite distortion: Formation of cusps II, Conform. Geom. Dyn. 11 (2007), 207-218. MR 2354095 (2009f:30055)
- 10.
- J. Väisälä, Lectures on n-dimensional quasiconformal mappings, Lecture Notes in Mathematics, vol. 229, Springer-Verlag, New York, 1971. MR 0454009 (56:12260)
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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
Email:
pekka.j.koskela@jyu.fi
Juhani
Takkinen
Affiliation:
Linnantie 8 C 21, 40800 Vaajakoski, Finland
Email:
juhani.takkinen@kolumbus.fi
DOI:
10.1090/S1088-4173-2010-00211-0
PII:
S 1088-4173(2010)00211-0
Keywords:
Cusp,
homeomorphism,
mapping of finite distortion
Received by editor(s):
April 17, 2010
Posted:
July 15, 2010
Additional Notes:
The first author was partially supported by the Academy of Finland grants nos. 120927 and 131477
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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