Geometry related to harmonic maps

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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