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In this paper we study the change of conformal structure induced by harmonic diffeomorphisms between Riemann surfaces. The main result of this paper is to answer the following question raised by R. Schoen (see [20]): Is it true that Riemann surfaces which are related by a surjective harmonic diffeomorphism are necessarily quasiconformally related? We show that there exists a pair of Riemann surfaces of infinite topological type, which are related by a surjective harmonic diffeomorphism but which are not quasiconformally related. Also we characterize when the above question has a positive answer in the case of Riemann surfaces of finite topological type.

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Caltech Authors  

Autor(es)

Markovic, Vladimir - 

Id.: 69834885

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Tipo de recurso: Article  -  PeerReviewed  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] http://resolver.caltech.edu/CaltechAUTHORS:20170505-160559819
[References] http://authors.library.caltech.edu/77244/

Fecha de contribución: 06-may-2017

Contacto:

Localización:
* Markovic, Vladimir (2002) Harmonic diffeomorphisms and conformal distortion of Riemann surfaces. Communications in Analysis and Geometry , 10 (4). pp. 847-876. ISSN 1019-8385 . http://resolver.caltech.edu/CaltechAUTHORS:20170505-160559819

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  1. $rec.titulo Very recently, Markovic, Lemm-Markovic and Benoist-Hulin, established the existence of a harmonic ma...

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