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Harmonic diffeomorphisms of noncompact surfaces and Teichmüller spaces
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Markovic, V. (Vladimir) (2002) Harmonic diffeomorphisms of noncompact surfaces and Teichmüller spaces. Journal of the London Mathematical Society, Vol.65 (No.1). pp. 103-114. doi:10.1112/S002461070100268X ISSN 0024-6107.
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Official URL: http://dx.doi.org/10.1112/S002461070100268X
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: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Teichmüller spaces, Riemann surfaces, Functions of several complex variables, Diffeomorphisms, Mappings (Mathematics) | ||||
| Journal or Publication Title: | Journal of the London Mathematical Society | ||||
| Publisher: | Cambridge University Press | ||||
| ISSN: | 0024-6107 | ||||
| Official Date: | February 2002 | ||||
| Dates: |
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| Volume: | Vol.65 | ||||
| Number: | No.1 | ||||
| Page Range: | pp. 103-114 | ||||
| DOI: | 10.1112/S002461070100268X | ||||
| Status: | Peer Reviewed | ||||
| Access rights to Published version: | Open Access (Creative Commons) |
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