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Harmonic diffeomorphisms and conformal distortion of Riemann surfaces

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

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.4310/CAG.2002.v10.n4.a7DOIArticle
http://www.intlpress.com/site/pub/pages/journals/items/cag/content/vols/0010/0004/a007/PublisherArticle
Additional Information:© 2002 International Press. Received November 15, 2000.
Issue or Number:4
Record Number:CaltechAUTHORS:20170505-160559819
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170505-160559819
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77244
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 May 2017 23:12
Last Modified:03 Oct 2019 17:55

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