在平面上谐波映射的范围上

IF 0.9 4区数学 Q2 Mathematics

Annales Academiae Scientiarum Fennicae-Mathematica Pub Date : 2019-03-18 DOI:10.5186/aasfm.2020.4550

J. G. Llorente

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引用次数: 0

摘要

1994年J. Lewis给出了经典小皮卡德定理的纯调和证明，证明了如果两个完整调和函数的联合值分布满足一定的限制条件，则它们必然是常数。我们将路易斯定理和调和刘维尔定理推广到调和映射在平面上的值域。

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On the range of harmonic maps in the plane

In 1994 J. Lewis obtained a purely harmonic proof of the classical Little Picard Theorem by showing that if the joint value distribution of two entire harmonic functions satisfies certain restrictions then they are necessarily constant. We generalize Lewis'theorem and the harmonic Liouville theorem in terms of the range of a harmonic map in the plane.

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来源期刊

Annales Academiae Scientiarum Fennicae-Mathematica 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annales Academiæ Scientiarum Fennicæ Mathematica is published by Academia Scientiarum Fennica since 1941. It was founded and edited, until 1974, by P.J. Myrberg. Its editor is Olli Martio. AASF publishes refereed papers in all fields of mathematics with emphasis on analysis.