Research on Complex Manifolds and Complex Analysis

首席调查员H.Sato研究了以下内容。1.他表示了所有八种典型的实型肖特基空间的形状，找到了作用于这些空间上的肖特基模群的生成元，并确定了肖特基模群的基本区域。这些结果已作为一篇题为《实类型二，三的经典肖特基群》的论文提交。2.给出了实型经典肖特基群的Jorgensen数的最佳下界。这些结果已作为一篇题为《实型经典肖特基群的Jogensen‘s不等式》的论文提交。此外，他还得到了关于Fuchsian肖特基群极限集的Hausdorff维数的一些结果。M.Taniguchi证明了Bloch范数收敛和Caratheodory意义下的几何收敛的等价性。Fujimoto将Beckenbach关于极小曲面的Nevanlinna理论推广到抛物黎曼曲面的极小曲面的情形。Y.Imayoshi通过曲面亏格估计了闭黎曼曲面之间非常数全纯映射的个数。N.Toda研究了复平面上全纯曲线的第二基本定理--亏量关系，改进了H.Cartan的结果。H.Yoshida在无界区域上得到了Dirichlet问题解的唯一性定理的一些结果。H.Watanabe定义并研究了具有分形边界的有界域的双层势。

Head investigator, H.Sato studied the following. 1.He represented the shape of all eight kinds of classical Schottky spaces of real type and found generators for the Schottky modular groups acting on the spaces and determined fundamental regions for the Schottky modular groups. The results have been submitted as a paper titled on "Classical Schottky groups of real type of genus two, III" . 2.He gives the best lower bounds of Jorgensen's numbers for classical Schottky groups of real type. The results have been submitted as a paper titled on "Jogensen's inequality for classical Schottky groups of real type " . Furthermore he obtained some results on the Hausdorff dimensions of the limit set of Fuchsian Schottky groups.M.Taniguchi showed the equivalence of the convergence in the Bloch norm and the geometric convergence in the sense of Caratheodory. H.Fujimoto extended the Nevanlinna theory for minimal surfaces due to Beckenbach to the case of the minimal surfaces for parabolic Riemann surfaces. Y.Imayoshi estimated the number of non-constant holomorphic mappings between closed Riemann surfaces by the genus of the surfaces. N.Toda investigated the second fundamental theorem, defect relation of holomorphic curves on the complex plane and inproved the results obtained by H.Cartan. H.Yoshida obtained some results on the uniqueness theorem of the solutions of Dirichlet problem in unbounded domains. H.Watanabe defined and studied the double layr potentials for a bounded domain with fractal boundary.