Geometry of Harmonicity

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・Bando studied the locally hyperbolically completeness of almost complex manifolds, and also showed the admissibility condition of Einstein-Hermitian metrics can be replaced by a condition which is easier to check.・Nishikawa proposed a framework for a differential geometric proof of Hartshorne conjecture, and obtained the fundamental results. He has also conducted the differential geometric study on the foliation structures of CR-manifolds.・Kenmotsu has extended his study of the periodicity of the surfaces of revolution with periodic mean curvature in the 3-dimensional Euclidean space to the higher dimensional case, and obtained an easier alternate proof of Hsian's result on the classification and construction of the hyper-surfaces of revolution of constant mean curvature.・Takagi studied the dynamics of reaction-diffusion systems of activator-inhibitor type which model morphogenesis in biology, and investigated how various conditions reflect on the location of spikes in the case of dimension 1.・Urakawa studied Yang-Mills theory and also conducted a study which relates graph theory and Riemannian geometry.・Sunada studied the random walks on graphs as an application of the discrete geometric analysis, and established several results on periodic random walks on crystal lattices applying the large deviation theory.・Horihata studied the initial-boundary value problem on Landau-Lifshitz-Gilbert (LLG) equation which is a model equation of magnetics, and constructed a weak solution. If the dimension is greater than 2, the weak solution converges to a constant in the infinit time provided the boundary value is a constant.