Nonlinear partial differntial equations related to geometric variational problems

与几何变分问题相关的非线性偏微分方程

• 批准号: 16540188
• 负责人: NAITO Hisashi
• 金额: $ 2.5万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16540188/
• 关键词: Differential Geometry; Harmonic Map; Variational Problems; Crystal Lattices; 非線形偏微分方程式; 熱方程式; Yang-Mills接続

The head investigator researches the geometric visualization of standard realized crystal lattices, which related with harmonic maps as an example of geometric variational problems. The standard realization of crystal lattices is defined by Kotani-Sunada, and it is considered as a realization of real crystals in nature. The definition of crystal lattice is an abelian covering of finite graph. The covering transformation group and/or the first fundamental group of a finite graph is its the first homology group and it is abelian. So, the crystal lattice is an abelian convering graph of a finite graph. The standard realization of a crystal lattices is defined using harmonic maps into Albanese Torus. Hence the definition is very abstract.The head investigator construct an application to visualize the standard realization of crystal lattices. Sunada constructs K4 Crystal Lattice as the standard realization of K4 Graph in 3-dimensional Euclidean space. Our application plays important role in calculations of the K4 real crystal with Carbon atoms

首席研究员研究标准实现晶格的几何可视化，这与调和图相关，作为几何变分问题的示例。晶格的标准实现是由Kotani-Sunada定义的，它被认为是自然界中真实晶体的实现。晶格的定义是有限图的阿贝尔覆盖。有限图的覆盖变换群和/或第一基本群是其第一同调群并且是交换群。因此，晶格是有限图的阿贝尔转换图。晶格的标准实现是使用阿尔巴尼环面的调和映射来定义的。因此这个定义非常抽象。首席研究员构建了一个应用程序来可视化晶格的标准实现。 Sunada构建了K4 Crystal Lattice作为K4 Graph在3维欧几里得空间中的标准实现。我们的应用程序在碳原子 K4 实晶体的计算中发挥着重要作用

项目成果

Star exponential functions as two-valued elementes

作为二值元素的星指数函数

• 发表时间: 2005
• 期刊: Progr.Math. 232
• 作者: M. A. Regusa;A. Tachikawa;Yoshiaki Maeda et al.
• 通讯作者: Yoshiaki Maeda et al.

Partial regularity of harmonic maps into Finsler spaces

调和映射到芬斯勒空间的部分正则性

• 发表时间: 2007
• 作者: Maria Alessandra Ragusa;Atsushi Tachikawa;Taeko Yamazaki;Michihiro Hashimoto and Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;T. Matsuyama and M. Ruzhansky;Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;Tokio Matsuyama;Tokio Matsuyama;松山 登喜夫;Taeko Yamazaki;山崎多恵子;山崎 多恵子;Atushi Tachikawa
• 通讯作者: Atushi Tachikawa

Partial reguraliry of the minimizer of quadratic functionals with VMO coefficients

带VMO系数的二次函数极小值的部分正则

• 发表时间: 2005
• 期刊: J.London Math.Soc.(2) 72
• 作者: M. A. Regusa;A. Tachikawa;Yoshiaki Maeda et al.;Atsushi Tachikawa et al.
• 通讯作者: Atsushi Tachikawa et al.

Partial regularity for the minimizer of harmonic maps into Finsler spaces

Finsler 空间中调和映射最小化的部分正则性

• 发表时间: 2007
• 作者: Y.Maeda;N.Miyazaki et al.;A. Tachikawa;A. Tachikawa
• 通讯作者: A. Tachikawa

Partial regularity for the minimizer of quadratic functional with VMO coefficients

带VMO系数的二次函数极小值的偏正则性

• 发表时间: 2005
• 期刊: J. London Math. Soc. (2) Vol.72(CONCERNED)
• 作者: M. A. Regusa;A. Tachikawa
• 通讯作者: A. Tachikawa