An area theorem for harmonic mappings with nonzero pole having quasiconformal extensions

Pub Date : 2024-03-29 DOI:10.1090/proc/16850

Bappaditya Bhowmik, Goutam Satpati

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Abstract

Let Σ H k ( p ) \Sigma _H^k(p) be the class of sense-preserving univalent harmonic mappings defined on the open unit disk D \mathbb {D} of the complex plane with a simple pole at z = p ∈ ( 0 , 1 ) z=p \in (0,1) that have k k -quasiconformal extensions ( 0 ≤ k > 1 0\leq k>1 ) onto the extended complex plane. In this article, we obtain an area theorem for this class of functions.

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具有准共形扩展的非零极谐波映射的面积定理

设 Σ H k ( p ) \Sigma _H^k(p)是一类定义在复平面的开放单位盘 D \mathbb {D} 上、在 z = p∈ ( 0 , 1 ) z=p \(0,1)处有一个简单极点、在扩展复平面上有 k k -等方扩展（0 ≤ k > 1 0\leq k>1 ）的保感单等调和映射。在本文中，我们得到了这一类函数的面积定理。

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