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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$\overline{\partial }$-energy integral and harmonic mappings


Author: Guowu Yao
Journal: Proc. Amer. Math. Soc. 131 (2003), 2271-2277
MSC (2000): Primary 58E20; Secondary 30C62
Published electronically: October 24, 2002
MathSciNet review: 1963777
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Abstract: In this paper, we discuss harmonic mappings on the unit disk with respect to any metric by using the $\overline{\partial }$-energy integral that was first introduced by Li in 1997 to treat quasiconformal harmonic mappings on the Poincaré disk, instead of the total energy integral. Some basic properties of harmonic mappings are given. Moreover, we give a new proof of the uniqueness theorem of Markovic and Mateljevic, which is more explicit and natural.


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Additional Information

Guowu Yao
Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Email: wallgreat@lycos.com

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06757-6
PII: S 0002-9939(02)06757-6
Keywords: Harmonic mapping, Main Inequality
Received by editor(s): February 20, 2002
Published electronically: October 24, 2002
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2002 American Mathematical Society