Markovic, Vladimir (2002) Harmonic diffeomorphisms and conformal distortion of Riemann surfaces. Communications in Analysis and Geometry, 10 (4). pp. 847-876. ISSN 1019-8385. doi:10.4310/CAG.2002.v10.n4.a7. 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 | |||||||||
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| Additional Information: | © 2002 International Press. Received November 15, 2000. | |||||||||
| Issue or Number: | 4 | |||||||||
| DOI: | 10.4310/CAG.2002.v10.n4.a7 | |||||||||
| 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: | 15 Nov 2021 17:29 |
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