Markovic, Vladimir (2002) Harmonic Diffeomorphisms of Noncompact Surfaces and Teichmüller Spaces. Journal of the London Mathematical Society, 65 (01). pp. 103-114. ISSN 0024-6107. doi:10.1112/S002461070100268X. https://resolver.caltech.edu/CaltechAUTHORS:20170505-153110854
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Abstract
Let g : M → N be a quasiconformal harmonic diffeomorphism between noncompact Riemann surfaces M and N. In this paper we study the relation between the map g and the complex structures given on M and N. In the case when M and N are of finite analytic type we derive a precise estimate which relates the map g and the Teichmüller distance between complex structures given on M and N. As a corollary we derive a result that every two quasiconformally related finitely generated Kleinian groups are also related by a harmonic diffeomorphism. In addition, we study the question of whether every quasisymmetric selfmap of the unit circle has a quasiconformal harmonic extension to the unit disk. We give a partial answer to this problem. We show the existence of the harmonic quasiconformal extensions for a large class of quasisymmetric maps. In particular it is proved that all symmetric selfmaps of the unit circle have a unique quasiconformal harmonic extension to the unit disk.
Item Type: | Article | |||||||||
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Additional Information: | © 2002 The London Mathematical Society. Received: 15 June 1999 Revision Received: 01 March 2001 Published: 01 February 2002 | |||||||||
Issue or Number: | 01 | |||||||||
Classification Code: | 2000 MSC: 32G15 | |||||||||
DOI: | 10.1112/S002461070100268X | |||||||||
Record Number: | CaltechAUTHORS:20170505-153110854 | |||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170505-153110854 | |||||||||
Official Citation: | Vladimir Markovic; Harmonic Diffeomorphisms of Noncompact Surfaces and Teichmüller Spaces. J London Math Soc 2002; 65 (1): 103-114. doi: 10.1112/S002461070100268X | |||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
ID Code: | 77242 | |||||||||
Collection: | CaltechAUTHORS | |||||||||
Deposited By: | Ruth Sustaita | |||||||||
Deposited On: | 09 May 2017 21:52 | |||||||||
Last Modified: | 15 Nov 2021 17:29 |
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