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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Topics in special functions. II


Authors: G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen
Journal: Conform. Geom. Dyn. 11 (2007), 250-270
MSC (2000): Primary 30C62; Secondary 33E05, 33E99
Published electronically: November 8, 2007
MathSciNet review: 2354098
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Abstract: In geometric function theory, conformally invariant extremal problems often have expressions in terms of special functions. Such problems occur, for instance, in the study of change of euclidean and noneuclidean distances under quasiconformal mappings. This fact has led to many new results on special functions. Our goal is to provide a survey of such results.


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Additional Information

G. D. Anderson
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: anderson@math.msu.edu

M. K. Vamanamurthy
Affiliation: Department of Mathematics, University of Auckland, Auckland, New Zealand
Email: vamanamu@math.auckland.nz

M. Vuorinen
Affiliation: Department of Mathematics, FIN-00014, University of Turku, Finland
Email: vuorinen@utu.fi

DOI: http://dx.doi.org/10.1090/S1088-4173-07-00168-3
PII: S 1088-4173(07)00168-3
Keywords: Schwarz Lemma, elliptic integral, distortion function, quasiconformal, Schottky, monotonicity, convexity, Teichm\"uller capacity
Received by editor(s): March 30, 2007
Published electronically: November 8, 2007
Additional Notes: The authors thank the Finnish Mathematical Society, the Finnish Academy of Sciences, and the Academy of Finland (grant no.\ 107317) for their support of this research.
Dedicated: Dedicated to Seppo Rickman and Jussi Väisälä.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.