Global Analysis for Geometric Structures and Topological Invariants

我们分别研究了几何结构和拓扑不变量的全局分析。芥川：他研究了紧化4流形上的Seiberg-Witten理论，自旋几何分析及其在K_hler曲面的Yamabe不变量上的应用。他得到了一些关于Yamabe不变量的开放问题的策略。佐托：他把2属实型的经典肖特基群划分为8类，然后得到了它们的基本定域和它们的肖特基空间的形状。Kumura：他研究了带加权测度的紧黎曼流形（M, g, upsilon）的谱距离，方法是利用它们的热核。他还研究了一族的紧性和{(M_i, g_i, upsilon_i)}闭包关于谱距离的结构。此外，他还将其结果应用于一些实例。Nakanishi：他研究了拓扑有限的二维双曲轨道的Teihm_ller空间的实解析结构。他将Teichm_ller空间实现为实代数曲面，并将这一结果应用于映射类群的表示问题和Weil-Petersson几何。Nayatani：他研究了复双曲等距离散群的不连续域上的正则度量。他特别定义了CR结构和伪厄米结构的四元数类似物，并将其应用于正则度量的研究。桥本：他研究了由黎曼曲面上的阿贝尔微分引起的几何结构。此外，他还从riemmainn曲面上射影结构的一元化的观点出发，给出了常平均曲率曲面的几何结构与表示公式之间的关系。

We studied global analysis for geometric structures and topological invariants, as follows respectively.Akutagawa : He studied on the theory of Seiberg-Witten theory on compact 4-manifolds, spin^c geome-try/analysis and its application to Yamabe invariants of K_hler surfaces. He obtained some strategies for open problems on Yamabe invariants.Sato : He classified classical Schottky groups of real type of genus two into eight categories, and then obtained the fundamental domains of them and the shapes of their Schottky spaces.Kumura : He studied on the spectral distance on compact Riemannian manifolds (M, g, upsilon) with weighted measure, by using their heat kernels. He also studied on compactness of a family of and the structure of the closure of {(M_i, g_i, upsilon_i)} with respect to the spectral distance. Moreover, he applied their results to some examples.Nakanishi : He studied on the real analytic structure of the Teihm_ller spaces of 2-dimensional hyperbolic orbifolds of topologically finite. He realized the Teichm_ller spaces as real algebraic surfaces, and applied this result to the problems on the representation of mapping class groups, and the Weil-Petersson geometry.Nayatani : He studied about the canonical metrics on the domains of discontinuity of discrete groups of complex-hyperbolic isometries. He defined quaternionic analogues of CR structures and pseudo-Hermitian sturctures paticularly, and applied them the study on the cannonical metrics.Hashimoto : He studied on geometric structures induced by the Abelian differentials on Riemann surfaces. Moreover, from the viewpoint of the reduction of monodoromy of the projective structures on a Riemainn surface, he also gave a relation between the geometric structures and representation formulas of constant mean curvature surfaces.