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Geometry of Harmonicity

调和几何

基本信息

批准号：
14340021
负责人：
BANDO Shigetoshi
金额：
$ 7.74万
依托单位：
Tohoku University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2005
项目状态：
已结题

项目摘要

・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.

Bando研究了几乎复流形的局部双曲完备性，并证明了Einstein-Hermite度量的可容许性条件可以用一个更容易检验的条件来代替。·Nishikawa提出了HartShorne猜想的一个微分几何证明框架，并得到了基本结果。他还对CR-流形的叶状结构进行了微分几何研究。·Kenmotsu将他对三维欧氏空间中具有周期平均曲率的旋转曲面的周期性的研究推广到高维情形，并得到了Hsian关于常平均曲率旋转超曲面的分类和构造结果的一个更容易的替代证明。·Takagi研究了在生物学中模拟形态发生的激活剂-抑制型反应-扩散系统的动力学，并研究了在维度1的情况下，各种条件如何反映尖峰的位置。·Urakawa研究了Yang-Mills理论，并进行了将图论与黎曼几何联系起来的研究。·Sunada作为离散几何分析的一个应用，研究了图上的随机游动，并应用大偏差理论建立了关于晶格上周期随机游动的几个结果。·Horihata研究了作为磁学模型方程的Landau-Lifshitz-Gilbert(LLG)方程的初边值问题，并构造了弱解。如果维度大于2，则在边值为常数的情况下，弱解在无限时间内收敛到常数。