A research of moving open Riemann surfaces

移动开黎曼曲面的研究

• 批准号: 09640183
• 负责人: MAITANI Fumio
• 金额: $ 1.92万
• 依托单位: Kyoto Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640183/
• 关键词: Riemann Surfaces; Quasiconformal mappings; Extremal slit mappings; Markov process; Evolution equation; Manifolds; Homeomorphic mappings; Mapping class groups

Our main subject is to analyze phenomenon which is caused on a moving Riemann surface, where analytic, geometric and algebraic structure are closely related. We study the theme multilateraly and get some results. In the field of analysis, the change of analytic structure under conformal welding of Riemann surface, and the behavior of Bergman metric under holomorphically quasiconformal deformation of Riemann surface are investigated, In the physical aspect, the asymptotic distribution of discrete eigenvalues near the bottom of the essential spectrum for 2-and 3-dimensional Pauli operators perturbed by electric potentials falling off at infinity and the non existence domain of positive eigenvalues of Schrodinger operator with von Neumann and Wigner potentials are studied. In the probability theory, an explicit formula for the Dirichlet form of a subordinated Markov process is given and it is shown that subordination preserves cores of Dirichlet forms. Some global properties for subordinated Markov processes are also studied. Especially, recurrence criteria and global capacitary inequalities are given. In multi resolution analysis, explicit construction of wavelet with a dilation factor n>2 is given. From a geometric point of view, the class of homeomorphism on a Riemann surface and its subclass of quasiconformal mappings are considered and it is shown that the pair is an (s-SIGMA)-manifold. Analytic torsion of line bundle on complex projective space is calculated by new approach. From an algebraic point of view, the compatibility of the filtration of mapping class groups of two surfaces pasted along the boundaries is studied.

我们的主要主题是分析在运动黎曼曲面上产生的现象，其中解析、几何和代数结构密切相关。我们对这一主题进行了多方面的研究，取得了一些成果。在分析领域，研究了黎曼曲面在保角焊接下解析结构的变化，以及在黎曼曲面全纯准共形变形下的Bergman度规行为；在物理方面，研究了受无穷大电位下降扰动的二维和三维Pauli算子在本质谱底部附近离散本征值的渐近分布以及具有von Neumann势和Wigner势的薛定谔算子正本征值的不存在域。在概率论中，给出了从属马尔可夫过程的Dirichlet形式的显式公式，并证明了从属保持Dirichlet形式的核。还研究了隶属马氏过程的一些全局性质。特别地，给出了常返性判据和全局容量不等式。在多分辨分析中，给出了伸缩因子为n&gt；2的小波的显式构造。从几何的角度考虑了黎曼曲面上的同胚类及其拟共形映射的子类，证明了这对映射是(S-Sigma)流形。用新方法计算了复射影空间上线丛的解析挠率。从代数的角度研究了沿边界粘贴的两个曲面的映射类群的滤子的相容问题。

项目成果

A.Nakaoka: "Exact solutions of evolution equation for linear viscoelastic medium" Theoretical and Applied Mechanics (Proc.of the 44th Japan Nat.Cong.for Appl.Mech.). 46. 95-108 (1997)

A.Nakaoka：“线性粘弹性介质演化方程的精确解”理论与应用力学（Proc.of the 44th Japan Nat.Cong.for Appl.Mech.）。

Tatsuhiko Yagasaki: "PL approximations of fiber preserving homeomorphisms of vector bundles" Tsukuba J.Math.21. 181-198 (1997)

Tatsuhiko Yagasaki：“保持矢量丛同态的纤维的 PL 近似”Tsukuba J.Math.21。

Mamoru Asada: "On a family of linear representations associated with Galor's representations in the automorphism groups of pro-l fundamental groups" Memo.Engi.and Design Kyoto Inst.Tech.45. 1-8 (1997)

Mamoru Asada：“关于与 Pro-l 基本群的自同构群中的 Galor 表示相关的一系列线性表示”Memo.Engi.and Design京都Inst.Tech.45。

Mamoru Asada: "On a family of linear representations associated with Galois representations in the automorphism groups of pro-l fundamental groups" Mem.Eng.Design Kyoto Inst.Tech.45. 1-8 (1997)

Mamoru Asada：“关于与 Pro-l 基本群的自同构群中的伽罗瓦表示相关的一系列线性表示”Mem.Eng.Design 京都 Inst.Tech.45。

M.Asada: "On a family of linear representations associated with Galois representations in the automorphism groups of pro-1 funcamental groups" Mem.Fac.Eng.Des.Kyoto Inst.Tech.45. 1-8 (1997)

M.Asada：“关于与 pro-1 funcamental 群的自同构群中的伽罗瓦表示相关的一系列线性表示”Mem.Fac.Eng.Des.Kyoto Inst.Tech.45。