QUANTITATIVE RESEARCH OF DEFICIENCIES OF MEROMORPFIC MAPPINGS AND EXCEPTIONAL MAPPINGS

亚形作图和异常作图缺陷的定量研究

• 批准号: 15540151
• 负责人: MORI Seiki
• 金额: $ 2.3万
• 依托单位: Yamagata University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540151/
• 关键词: value distribution theory; meromorphic mapping; defect; unicity theorem; hypersurface; complex dynamical system; complex projective space; function space; 力学系; ジュリア集合; カオス力学系

The head investigator Mori researched a sparsity of meromorphic mappings with defects. He obtained elimination theorems of defects of hypersurfaces or rational moving targets of a meromorphic mapping into P^n(C) by a small deformation, and he also proved that mappings without defects are dense in a space of transcendental meromorphic mappings. He and an investigator Aihara also obtained results that for any hypersurface of degree d on P^n(C), we can construct an algebraically nondegenerate meromorphic mapping with a preassaigned deficiency in an interval (0,α), where α>0 depends only on d. Mori also studied on uniqueness theorems of meromorphic functions. There are many results on uniqueness sets, but it seems that there are few results on uniqueness domains. We are going to find an unbounded domain in C such that a uniqueness theorem holds under the condition restricted on the domain. Mori, Lin and Tohge gave a uniqueness theorem under the condition restricted on an angular domain, an … More d the paper was submitted. An investigator Aihara obtained several conditions on the inverse image of a divisor under meromorphic mappings for which mappings are algebraically dependent, and he also obtained a condition under which two analytic ramified covering spaces are identical. This is a geometric extension of a uniqueness theorem of algebroid functions. Nakada investigated a complex dynamics of Blachke products like rational functions, especially, an estimate of a Hausdorff dimension and the invariance of Julia set under Euclidean congruent transformation. Sekigawa investigated a limit set of a sequence of Moebius transformations acting on C, and also he treated Moebius transformations acting on a general dimension space. He also studied an expression of Moebius transformations using Cliford matrix, and its applications. Kawamura studied an orbit of probabilistic density function, and also he gave a proof of a properties of topological conjugate maps on a group of Tent maps, after computer simulation. Sato gave a generalization of relation between Jacobian orthogonal system and an operators on a function space and an operators on Hankel transformations. Mizuhara proved a weak decomposition theorem related to a function on a generalized Morrey space and Block and Calderon-Zygmund operators. Less

调查员莫里（Mori）研究了有缺陷的杂物映射的稀疏性。他通过较小的变形得出了脱落表面缺陷或合理移动靶标的消除定理，他还通过较小的变形映射到p^n（c）中，他还证明，没有缺陷的映射在超源物质映射的空间中密集。 HE和研究者Aihara还获得了结果，即对于p^n（c）上D度的任何超表面，我们可以在间隔（0，α）中构建具有预先宣布的缺陷的代数非等级的Meromormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormorormormorormormorormormormormormorormormormormormormormorormormorormormorormormorormorormormorormorormorormorormorormorormorormorormorormorormorormorormorormorqu，，其中α> 0仅取决于d。 Mori还研究了Meromorormorphic函数的唯一定理。独特性集有很多结果，但是在唯一性域上似乎几乎没有结果。我们将在C中找到一个无限的域，以便在限制域的条件下存在唯一性定理。 Mori，Lin和Tohge在限制在角域的条件下给出了独特的定理，并且提交了更多纸。研究者Aihara在Meromormormormormormormormormormormormormorphic映射下获得了几种条件，该映射的映射是代数依赖的，他还获得了一个条件，在该条件下，两个分析性分析后的覆盖空间相同。这是代数函数唯一定理的几何扩展。 Nakada研究了Blachke产品（例如理性函数）的复杂动力学，特别是对Hausdorff维度的估计值以及在Euclidean同等转化下设置的Julia的不变性。 Sekigawa研究了作用于C的一系列Moebius变换序列，他还处理了作用于一般维空间的Moebius变换。他还使用Cliford矩阵及其应用研究了Moebius转换的表达。川村研究了概率密度函数的轨道，并且在计算机模拟后，他还证明了一组帐篷地图上拓扑结合图的特性。 Sato对Jacobian正交系统与操作员在功能空间与Hankel转换的操作员之间的关系进行了概括。瑞马哈拉（Mizuhara）证明了与广义的莫雷空间和块和卡尔德隆·齐格蒙德运算符上的功能相关的弱分解定理。较少的

项目成果

RECENT TOPICS IN UNIQUENESS PROBLEM FOR MEROMORPHIC MAPPINGS

• DOI: 10.1007/1-4020-7951-6_13
• 发表时间: 2004
• 作者: Yoshihiro Aihara

Deficiencies of meromorphic mappings for hypersurfaces

超曲面亚纯映射的缺陷

• 发表时间: 2005
• 期刊: J. Math. Soc. Japan 47
• 作者: Y.Aihara;S.Mori
• 通讯作者: S.Mori

Factorization of functions in H^1(R^n) and generalized Morrey spaces

H^1(R^n) 和广义 Morrey 空间中函数的因式分解

• 期刊: Math. Nachr. (掲載予定)
• 作者: Komori Yasuo;Mizuhara Takahiro
• 通讯作者: Mizuhara Takahiro

Lorentz multipliers for Hankel transforms

汉克尔变换的洛伦兹乘子

• 发表时间: 2004
• 期刊: Scientiae Mathematicae Japonicae 59
• 作者: M.Belarbi;萬代武史;M.Mechab;Aihara Yoshihiro;K.Igari;Sato Enji
• 通讯作者: Sato Enji

Uniqueness problem for meromorphic mappings under conditions on the preimages of divisors

除数原像条件下亚纯映射的唯一性问题

• 发表时间: 2004
• 期刊: Advanced Studies in Pure Mathematics, Complex Analysis in Several Variables,(Mathematical Society of Japan) 42
• 作者: M.Belarbi;萬代武史;M.Mechab;Aihara Yoshihiro;K.Igari;Sato Enji;Mori Seiki;Aihara Yoshihiro;Aihara Yoshihiro;Sato Enji;T.Sadamatsu;Seiki Mori;Yoshihiro Aihara
• 通讯作者: Yoshihiro Aihara