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

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-03-29 DOI:10.1090/proc/16850

Bappaditya Bhowmik, Goutam Satpati

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引用次数: 0

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.