Geometry of Harmonicity

Bando研究了在当地最复杂的多重性方面的高度完整性，并展示了爱因斯坦-赫敏计量学的适应性状况，也可以通过一种情况来替换，以确定哪一种情况很容易。Nishikawa提出了一个框架，用于Hartshorne概念的不同几何学证明，并获得了基本结果。他还对CR-歧管结构的形成结构进行了不同的几何学研究。Kenmotsu在3-dimensional Euclidean空间中扩展了对表面革命周期性的研究，并在高尺寸情况下获得了对Hsian的结果的更容易的替代性证明，在分类和构造的超表面革命的恒定平均曲线中发现了一个更容易的替代证据。Takagi研究了活性剂-抑制剂类型的反应扩散系统的动力学，并研究了生物学模型形态发生学中的各种情况对尖峰位置的反映。乌拉川研究了杨-米尔斯理论，也研究了关系图理论和利曼尼亚几何学。Sunada在图形上研究了随机行走作为离散几何分析的应用，并在晶体晶格上应用大偏差理论上建立了若干结果。Horihata研究了Landau-Lifshitz-Gilbert（LLG） equation的初始边界值问题，它是一个磁性equation的模型，并构建了一个弱解决方案。如果尺寸大于2，那么较弱的解决方案转换在最短时间内提供了恒定的边界值也是恒定的。

・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.