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| Authors: | Guowu Yao |
| Affiliation: | School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China |
| 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. |
| Keywords: | Harmonic mapping Main Inequality |
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