Geometry of Harmonicity

调和几何

• 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
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14340021/
• 关键词: Futaki invariant; complex Finsler manifold; harmonic maps; energy functional; mean curvature; reaction-diffusion system; heat kernel; crystal lattice; 活性因子・抑制因子型反応拡散系; 概複素構造; ヤン・ミルズ接続; シンプレクティック多様体; ケーラー多様体; 解析的連接層; 安定性; 複素フィンスラー空間; 回転面

・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X歧管的倍增性，还显示了可接纳性的条件 - 温米三分之二的条件可以用ESIER进行检查。多种多样的人在三维欧几里得太空空间中对革命表面的周期性进行了研究平均曲率研究了尖峰的各种条件在维度1的情况下landau-lifshitz-gilbert（LLG）方程的初始界价值是磁性的模型方程，如果尺寸大于2个，则构建了一个弱解。

项目成果

Surfaces With Constant Mean Curvature

• DOI: 10.1090/mmono/221
• 发表时间: 2003-10
• 作者: K. Kenmotsu

An obstruction for Chem class forms to be harmonic

Chem 类形式和谐的障碍

• 期刊: Kodai Math.J. (accepted)
• 作者: W.-M.Ni;K.Suzuki;I.Takagi;H.Nakamura;H.Nakamura;S.Bando
• 通讯作者: S.Bando

K.Kenmotsu: "Surfaces of revolution with periodic mean curvature"Osaka Jour.Math.. 40. 687-696 (2003)

K.Kenmotsu：“具有周期平均曲率的旋转表面”Osaka Jour.Math.. 40. 687-696 (2003)

Yang-Mills connections in homogeneous principal fiber bundles

均匀主纤维束中的 Yang-Mills 连接

• 发表时间: 2004
• 期刊: International J.Pure Applied Mathematics 10
• 作者: N.Shimono;N.Koyama;M.Kawaguchi;H.Urakawa;H.Urakawa;H.Urakawa;H.Urakawa;H.Urakawa;H.Urakawa
• 通讯作者: H.Urakawa

Globalsolutions to a one-dimensional nonlinear parabolic system modeling colonial formation by chemotactic bacteria

模拟趋化细菌菌落形成的一维非线性抛物线系统的全局解决方案

• 期刊: "Asymptotic Analysis and Singularity", Advanced Studies in Pure Mathematics (to appear)
• 作者: K.P.Htoo;M.Mimura;I.Takagi
• 通讯作者: I.Takagi