Complex manifolds and Teichmuller spaces

这位首席研究员一直在研究复杂流形上的几何对象和解析对象，特别是在Riemann曲面和TeichMuller空间上。特别地，他利用复分析、Klein群、TeichMuller空间，研究了复流形之间的全纯映射的Douady空间，全纯映射的个数估计，调和映射与全纯映射之间的关系等。设Hol(R，S)是亏格为g的闭黎曼曲面R到亏格为g‘的闭黎曼曲面S的所有非常数全纯映射的集合，且具有g’，(2&lt；小于等于&gt；g‘&lt；小于或等于&gt；g’)。然后利用拓扑数据g和g‘得到了Hol(R，S)中元素个数的估计。它的证明方法是利用双曲几何、Kleinan群和复分析来估计面积。因此，该方法同样适用于双曲型开Riemann曲面的情况。黎曼曲面与全纯二次微分之间的调和映射与…密切相关更多的爱德。从这一角度出发，研究了黎曼曲面之间调和映射与全纯映射之间的关系。在一定的Komori研究的TeichMuller空间的半代数刻画下，证明了调和映射成为全纯或反全纯的。Okumura得到了TeichMuller空间的整体实解析角参数。Sakan考虑了非拟共形调和扩张。Taniguchi证明了泛TeichMuller空间的Bloch拓扑等价于Caratheodory意义下的几何收敛。Kamiya利用Heisenberg变换研究了PSU(1，2，C)的离散子群。Masaoka得到了覆盖曲面调和维数的一些重要结果。Maitani考虑了Riemann曲面的最优嵌入问题，野口得到了函数域上Cartan-Nvalinna定理的第二个主要定理，并将其应用于有理点的有限性定理。Toda得到了非退化全纯曲线的基本不等式。Mori在值分布定理中构造了C^n到P^n(C)的亚纯映射的一些重要例子。Nishio得到了多温度的平均值性质。较少

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