\overline{∂}-energy integral and harmonic mappings

Yao, Guowu

doi:10.1090/S0002-9939-02-06757-6

$\overline {\partial }$-energy integral and harmonic mappings
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Proc. Amer. Math. Soc. 131 (2003), 2271-2277 Request permission

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 Marković and Mateljević, which is more explicit and natural.

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