图像具有有限球面面积的亚纯函数

IF 0.7 3区数学 Q2 MATHEMATICS

Studia Mathematica Pub Date : 2022-01-28 DOI:10.4064/sm220618-19-3

O. Ivrii

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引用次数: 0

摘要

在本文中，我们研究了域$\Omega\subet\mathbb｛C｝$上的亚纯函数，该域的图像具有有限的球面面积，用多重性计数。本文由两部分组成。在第一部分中，我们证明了亚纯函数序列的极限是在$\Omega$并球树上自然定义的。在第二部分中，我们证明了集合$E\subet\Omega$是可移除的，当且仅当它对于极值距离是可忽略的。

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On meromorphic functions whose image has finite spherical area

In this paper, we study meromorphic functions on a domain $\Omega \subset \mathbb{C}$ whose image has finite spherical area, counted with multiplicity. The paper is composed of two parts. In the first part, we show that the limit of a sequence of meromorphic functions is naturally defined on $\Omega$ union a tree of spheres. In the second part, we show that a set $E \subset \Omega$ is removable if and only if it is negligible for extremal distance.

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来源期刊

Studia Mathematica 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

5 months

期刊介绍： The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.