The research of the behavior of geodesics

测地线行为研究

• 批准号: 14540091
• 负责人: TANAKA Minoru
• 金额: $ 1.79万
• 依托单位: Tokai University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 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-14540091/
• 关键词: cut locus; geodesic; fractal set; Hausdorff dimension; surface of revolution; torus; ellipsoid; cusp; フラクタル次元; エントロピー次元; エントリピー次元; ロボット工学

1) The structure of the cut locus of a standard torus of revolution in Euclidean space was completely determined by J.Gravesen, S.Markvorsen, R.Sinclair and M.Tanaka (the head investigator). Furthermore the structure of a family of torus of revolution containing the standard tori.2) R.Sincalir and M.Tanaka had a conjecture of the upper bound of the number of endpoints of a cut locus on a surface of revolution experimentally. R.Sinclair checked it by making use of his computer programming.3) M.Tanaka proved that the cut locus of a surfase whith real analytic Riemannian metric has at least four cusps if the surface is homeomorphic to a sphere.4) T.Matsuyama and M.Tanaka treated the outside problem of the wave equation. We obtained the L^2 estimates of the solution and proved the nondecay of the energy of the solution. Furthermore M.Tanaka proved that the boundary of the convex hull of a smooth hypersurface in any dimensional Euclidean space is only continuously differentiable, but not smooth and gave a counterexample of it.

1）J.Gravesen，S.Markvorsen，R.Sinclair和M.Tanaka（首席研究员）完全确定了欧几里得空间中革命标准旋转曲线的切割基因座的结构。此外，一个包含标准托里的革命家族的结构。2）R.Sincalir和M.Tanaka对革命表面上切割基因座的端点数量的上限进行了猜想。 R.Sinclair通过使用他的计算机编程来对其进行检查。3）M.Tanaka证明，如果表面对球体同同态，则表面效果的切割基因座至少具有四个cusp。我们获得了溶液的l^2估计值，并证明了溶液能量的无周期。此外，M.Tanaka证明了在任何维欧几里得空间中平滑性超表面的凸壳的边界仅是连续的，但不是平滑的，但没有平滑，并给出了反例。

项目成果

Almost periodic oscillations of suspended string under quasiperiodic linear force

拟周期线性力作用下悬弦的近似周期振荡

• 发表时间: 2005
• 期刊: Journal of Mathematical Analysis and Applications Vol.303
• 作者: M.Tanaka;M.Yamaguchi;M.Yamaguchi
• 通讯作者: M.Yamaguchi

K.Shiohama: "The Geometry of Total Curvature on Complete Open surfaces"Cambridge University Press. 284 (2003)

K.Shiohama：“完全开放曲面上总曲率的几何”剑桥大学出版社。

Interdependent preferences with a continuum of agents

具有连续体的相互依赖的偏好

• 发表时间: 2005
• 期刊: Journal of Mathematical Economics 41巻・6号
• 作者: M.Tanaka;M.Tanaka;M.Tanaka;M.Yamaguchi;M.Yamaguchi;M.Noguchi
• 通讯作者: M.Noguchi

The set of poles of a two-sheeted hyperboloid

两片双曲面的极点组

• 发表时间: 2002
• 期刊: Experimental Mathematics 241巻・2号
• 作者: T.Matsuyama;M.Tanaka;M.Yamaguchi;M.Yamaguchi;J.Lu;J.Lu;R Sineclair;R.Sinclair
• 通讯作者: R.Sinclair

K.Shiohama: "Compactification and maximal diameter theorem for noncompact manifolds with radial curvature bounded below"Math. Zeit.. 241・2. 341-351 (2002)

K. Shioham：“具有以下边界的非紧流形的紧致性和最大直径定理”Zeit.. 241・2（2002）。