Geometry related to harmonic maps

表面理论(Miyaoka，Koiso，Sato，Masuda，Cheng)，超曲面理论(Miyaoka，Miyaoka)，可积系统理论(Miyaoka，Ito，Ohnita，Udagawa)，格和图上调和映射理论(Kotani)，规范理论调和映射理论(Ohnita，Hashiguchi)，李群与对称空间理论(Hattori，Tanaka)，随机值分布理论(Atsuji)，基于Seiberg-Witten方程的微分拓扑不变量(Futaki)，理想乘子集(Tsuji)的应用构造了从紧Riemann曲面到5维球面的非共形调和映射的整体形变实例，给出了零性的一个较低估计，并给出了三维球面中的常平均曲率曲面与到2维球面的一对非共形调和映射之间的整体对应.她展示了IS…的同质性利用等谱原理和Singer定理，引进了Ferapontov关于流体力学哈密顿系统可积性理论关系的结果，以及Terng-Uhlenbecks通过泊松作用量对散射方法、谱系和Backlund变换的解释。Futaki利用Seiberg-Witten方程研究了Kahler-Einstein度量或正标量曲率度量存在的障碍。将Liouvill-Arnold定理推广到具有奇异的可逆系统等。Ohnita研究了调和映射规范理论方程的解的模空间构造了一族Hitchin自对偶方程解的超Khler模的复Lagrange子流形。Kotani研究了晶格上调和映射的行为，讨论了热核在无限时刻的渐近展开，并讨论了它与阿尔巴尼亚映射的关系。Atusji应用了随机微积分中全纯映射和调和映射的值分布，推广了Casorati-Weerstrass型定理，关于Nevanlinna亚纯函数的对数微分引理等

Main results in the surface theory (Miyaoka, Koiso, Sato, Masuda, Cheng), the theory of hypersurfaces (Miyaoka), the theory of integrable systems (Miyaoka, Ito, Ohnita, Udagawa), the theory of harmonic maps on lattices and graphs (Kotani), the theory of Gauge theoretic harmonic maps (Ohnita, Hashiguchi), the theory of Lie group and symmetric spaces (Hattori, Tanaka), stochastic value distribution theory (Atsuji), Differential topological invariant via Seiberg-Witten equation (Futaki), application of multiplier ideal sheaves (Tsuji), are as follows :Miyaoka characterized non-conformal harmonic maps as components of minimal surfaces, constructed examples of global deformations of non-conformal harmonic maps from compact Riemann surfaces into 5-dimensional sphere, giving a lower estimate of the nullity, and gave a global correspondence between constant mean curvature surfaces in 3-dimensional sphere and a pair of non-conformal harmonic maps into 2-spheres. She showed the homogeneity of is … More oparametric hypersurfaces with six principal curvatures, applying the isospectral principle and Singer's theorem, introduced Ferapontov's results on the relation with the integrability theory of Hamiltonia system of hydrodynamic type, and Terng-Uhlenbecks' explanation of scattering method, hierarchy, and Backlund transformation via the Poisson actions.Futaki investigated the obstructions to the existence of Kahler-Einstein metrics or positive scalar curvature metrics, by using Seiberg-Witten equation.Ito extended Liouvill-Arnolds' theorem into sustems such as reversible system which has singularities.Ohnita investigated the moduli space of the solution of Gauge-theoretic equation of harmonic maps, and constructed a family of complex Lagrangean submanifolds of the hyper-Khler moduli of the solution of Hitchin's self-dual equations.Kotani investigated the behavior of harmonic maps on crystal lattices, of the asymptotic expansion of heat kernels at infinite time, and discussed with the relation to Albanese maps.Atusji applied value distribution of holomorphic and harmonic maps in stochastic calculus, and generalized Casorati-Weierstrass type theorem, lemma on logarithmic differential for Nevanlinna meromorphic function, etc. Less