-energy integral and harmonic mappings

Author:
Guowu Yao

Journal:
Proc. Amer. Math. Soc. **131** (2003), 2271-2277

MSC (2000):
Primary 58E20; Secondary 30C62

DOI:
https://doi.org/10.1090/S0002-9939-02-06757-6

Published electronically:
October 24, 2002

MathSciNet review:
1963777

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we discuss harmonic mappings on the unit disk with respect to any metric by using the -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:
https://doi.org/10.1090/S0002-9939-02-06757-6

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