Some Properties of the Beurling-Ahlfors Extension

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Abstract

In this paper, we study the Beurling-Ahlfors extensions and prove two results. The first variation of the Beurling-Ahlfors extension is not always harmonic; the Beurling-Ahlfors extension of a quasi-symmetric mapping is not always harmonic.

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Beurling-Ahlfors extension first variation harmonic map.
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Some Properties of the Beurling-Ahlfors Extension. (2021). Communications in Mathematical Research, 27(4), 289-296. https://www.global-sci.com/index.php/cmr/article/view/8704