共查询到19条相似文献,搜索用时 281 毫秒
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在本文研究了亚纯函数族的正规族问题,利用Zalcman引理的方法,获得了亚纯函数族的几个正规定则.并改进了顾永兴和Bergweiler的结果. 相似文献
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《数学的实践与认识》2017,(20)
主要讨论涉及分担值的两个相关亚纯函数族的正规性,推广刘晓俊,李三华和庞学诚关于两族亚纯函数分担4个值的一个结果,给出了两个相关亚纯函数族分担3个值和2个值情况的正规定则. 相似文献
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研究函数族的正规性定则是复变函数论中的一个重要且有意义的工作,本文通过引进多元K-拟亚纯函数(或K-全纯函数)的定义,得到了多元K-拟亚纯函数(或K-全纯函数)族的一个正规定则,据此讨论了多元纯函数(族的若干正规性定则。 相似文献
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本文建立了如下定则:设{f(z)}为区域D内亚纯函数族,ι为一正整数.若对于族中任一函数f(z)在D内满足f(z)≠0,则亚纯函数族{f(z))在D内正规. 相似文献
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单复变中的Pang-Zalcman引理是研究亚纯函数正规族问题的重要工具.本文将该引理推广至多复变全纯函数的情形.作为应用建立了多复变全纯函数族的正规定则,改进和推广了相关结果. 相似文献
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研究了涉及分担值的亚纯函数正规族,得到了几个涉及分担值的定理,推广了前人的一些结果. 相似文献
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In this paper, we investigate the general normality criteria for a family of meromorphic functions using a geometric method.
We obtain the necessary and sufficient conditions used for determining the normality of a family of meromorphic functions
and some normal criteria on the family of meromorphic functions with shared set by using the fundamental theorem of a covering
surface. 相似文献
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《数学研究通讯:英文版》2017,(4):347-358
In this paper,by using the idea of truncated counting functions of meromorphic functions,we deal with the problem of uniqueness of the meromorphic functions whose certain nonlinear differential polynomials share one finite nonzero value. 相似文献
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进一步讨论亚纯函数的k阶导数具有公共小函数的唯一性问题,得到两个亚纯函数唯一性问题的结果,改进了李平的有关结果. 相似文献
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邱淦弟 《数学物理学报(A辑)》2004,24(2):246-250
该文主要讨论亚纯函数的导数具有四个公共小函数时的唯一性问题,考虑了Nevanlinna 四值定理在亚纯函数的导数具公共小函数时的情形,推广并改进了作者近期的一个结果。
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Atsushi Atsuji 《Potential Analysis》2018,48(1):85-113
We discuss the value distribution of Borel measurable functions which are subharmonic or meromorphic along leaves on laminations. They are called leafwise subharmonic functions or meromorphic functions respectively. We consider cases that each leaf is a negatively curved Riemannian manifold or Kähler manifold. We first consider the case when leaves are Riemannian with a harmonic measure in L.Garnett sense. We show some Liouville type theorem holds for leafwise subharmonic functions in this case. In the case of laminations whose leaves are Kähler manifolds with some curvature condition we consider the value distribution of leafwise meromorphic functions. If a lamination has an ergodic harmonic measure, a variant of defect relation in Nevanlinna theory is obtained for almost all leaves. It gives a bound of the number of omitted points by those functions. Consequently we have a Picard type theorem for leafwise meromorphic functions. 相似文献
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《Journal of Number Theory》1987,25(2):220-229
We extend the Schneider-Lang theorem concerning algebraic values of meromorphic functions on the complex plane to meromorphic functions on punctured Riemann surfaces by using Jensen's formula for Riemann surfaces. 相似文献
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In this paper, general modular theorems are obtained for meromorphic functions and their derivatives. The related criteria
for normality of families of meromorphic functions are proved.
Research supported by the National Science Foundation of China 相似文献