Complex manifolds and Teichmuller spaces

复流形和 Teichmuller 空间

基本信息

批准号：
08304014
负责人：
IMAYOSHI Yoichi
金额：
$ 9.22万
依托单位：
Osaka City University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08304014/
关键词：
Teichmuller space complex manifold Riemann surface Kleinian group quasiconformal mapping several complex varialbles potential theory value distribution theory 多変数関数論値分布論等解像論

项目摘要

The head investigator has been studying geometric and analytic objects on complex manifolds, especially on Riemann surfaces and Teichmuller spaces. In particular, using complex analysis, Kleinian groups, Teichmuller spaces, he studied Douady spaces of holomorphic maps between complex manifolds, estimates of numbers of holomorphic maps, relations between harmonic maps and holomorbhic maps, and so on. Let Hol (R,S) be the set of all non-constant holomorphic maps of a closed Riemann surface R of genus g to a closed Riemann surface S of genus g' with g', (2<less than or equal>g'<less than or equal>g'). Then an estimate of the number of elements in Hol (R,S) is obtained by topological data g and g'. Its method of proof is an area estimate by using hyperbolic geometry, Kleinian groups, and complex analysis. So this method is also applicable to the case of open Riemann surfaces of hyperbolic type. Harmonic maps between Riemann surfaces and holomorphic quadratic differentials are closely relat … More ed. From this point of view, relations between harmonic maps and holomorphic maps between Riemann surfaces are considered. It is proved that harmonic maps become holomorphic or anti-holomorphic under a certaiKomori studied semialgebraic description of Teichmuller space. Okumura obtained global real analytic angle parameters for Teichmuller spaces. Sakan considered non-quasiconformal harmonic extention. Taniguchi proved that Bloch topology of the universal Teichmuller space is equivalent to the geometric convergence in the sense of Caratheodory. Kamiya studied discrete subgroups of PSU (1,2, C)with Heisenberg translations. Masaoka obtained some important results on harmonic dimension of covering surfaces. Maitani considered ploblems on optimal embedding of Riemann surfaces.Noguchi obtained the second main theorem of Cartan-Nevalinna theorem over function fields and its application to finiteness theorem for rational points. Toda obtained the fundamental inequality for non-degenerate holomorhic curves. Mori constructed some important examples for meromorphic maps of C^n into P^n (C) in the value distribution theorem. Nishio got a mean value property for polytemperatures. Less

首席研究者一直在研究复杂歧管上的几何和分析对象，尤其是在Riemann表面和Teichmuller空间上。特别是，使用复杂的分析，克莱恩群，teichmuller空间，他研究了复杂的歧管之间的霍明态图的杜迪空间，霍明态图的估计值，谐波图与霍尔态图之间的关系等等。令HOL（R，S）为G'属G'属的封闭的Riemann表面R的所有非恒定性全态图的集合（2 <少于或等于> g'<小于或等于> g'）。然后，通过拓扑数据g和g'获得了HOL（R，S）中元素数量的估计。它的证明方法是使用双曲线几何形状，克莱尼亚组和复杂分析的区域估计。因此，此方法还适用于双曲线类型的开放式Riemann表面。 Riemann表面和骨膜二次差异之间的谐波图密切相关……更多。从这个角度来看，考虑了Riemann表面之间的谐波图与塑性图之间的关系。事实证明，在teichmuller空间的Certaikomori Sutiood Semialgebraic描述下，谐波图成为骨形或抗塑形的。 Okumura获得了Teichmuller空间的全局实际分析角度参数。 Sakan认为非质量谐波扩展。 Taniguchi证明了通用Teichmuller空间的Bloch拓扑相当于Caratheodory的几何融合。卡米亚（Kamiya）研究了带有海森贝格（Heisenberg）翻译的PSU（1,2，c）的离散子组。 Masaoka在覆盖表面的谐波维度上获得了一些重要的结果。 Maitani考虑了Riemann表面最佳嵌入的拼图。Noguchi获得了cartan-Nevalinna定理的第二个主要理论，而不是功能领域，以及其在理性点的有限定理中的应用。 Toda获得了非统计全态曲线的基本不平等。莫里（Mori）在值分布定理中构建了一些C^n中的Meromormormormormormorphic图中的重要示例。 Nishio获得了多晶的平均价值属性。较少的