ON THE RANGE OF HARMONIC MAPS IN THE PLANE

被引：0

作者：

Llorente, Jose G. ^{[1
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Spain

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2020年 / 45卷

关键词：

Picard theorem; Liouville theorem; harmonic map; harmonic function; harmonic polynomial; PICARDS THEOREM;

D O I：

10.5186/aasfm.2020.4550

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give geometrical conditions on the range of a harmonic map in the plane implying that it is constant. This approach is motivated and generalizes Lewis' proof of the classical Little Picard Theorem. We also provide results extending the harmonic Liouville Theorem and the planar version of a result by Murdoch and Kuran.

引用

页码：915 / 930

页数：16

共 15 条

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