Uniformization Theorems on Manifolds

Futaki研究了Kaehler-Einstein度量的存在性、代数流形在Mumford意义上的稳定性和Futaki特征的非平凡性之间的关系。Tanno研究了欧几里得（m+1）空间中完全稳定极小超曲面上不存在L^2调和形式的猜想，并对m<5给出了肯定证明。Ishii构造了任意非退化超曲面奇点的正则模型、极小模型和对数正则模型。她还建立了环缘品种除数的最小模型。她构造了一个反例来反驳里德关于标准奇点的猜想。Tsuji用奇异度量分析了正则环的结构。他考虑了一般类型代数变体的模空间的构造。Hattori考虑了Riemann表面上由射影结构诱导的完整群是离散的情况，并证明了只有当它们稳定时才会出现伪Fuchsian群。

Futaki studied on the relationship between the existence of Kaehler-Einstein metrics, stability of algebraic manifolds in the sense of Mumford and the nontriviality of the Futaki character.Tanno studied on the conjecture that there would not exist any L^2 harmonic forms on complete stable minimal hypersurfaces in Euclideam (m+1)-space, and proved affirmatively for m<5.Ishii constructed canonical models, minimal models and logarythmic canonical models for arbitrary nondegenerate hypersurface singularities. She also constructed minimal models for divisors of toric varieties. She construted a counter-example to a conjecture of Reid concerning canonical singularities. Tsuji analyzed the structure of canonical rings using singular metrics. He considered a construction of the moduli spaces of algebraic varieties of general type.Hattori considered the case where the holonomy groups induced by the projevtive structures on Riemann sufaces are discrete, and showed that only pseudo Fuchsian groups can appear when they are stable.