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Harmonic Diffeomorphisms of Noncompact Surfaces and Teichmüller Spaces

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. 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
Related URLs:
URLURL TypeDescription
https://doi.org/10.1112/S002461070100268XDOIArticle
https://academic.oup.com/jlms/article/65/1/103/873945/Harmonic-Diffeomorphisms-of-Noncompact-SurfacesPublisherArticle
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
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:03 Oct 2019 17:55

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