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Mathematical Sciences: Spectral Geometry and Inverse Problems

Mathematical Sciences: Spectral Geometry and Inverse Problems
数学科学:谱几何和反问题
批准号:
9203529
负责人:
Peter Perry
金额:
$12.3万
依托单位国家:
美国
项目类别:
Continuing Grant
财政年份:
1992
资助国家:
美国
项目状态:
已结题
起止时间:
1992-06-01 至 1996-05-31

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中文摘要
翻译
本研究涉及光谱几何的三个领域:(1)Kleinian群的光谱几何、迹公式和行列式;(2)等电黎曼流形的有限性和紧性定理;(3)自由边界问题的光谱几何。研究了任意几何有限双曲等距离散群的迹公式的发展和拉普拉斯行列式的研究。重点是协无穷体积群,目标是从几何上理解散射算子的极点,并研究拉普拉斯和塞尔伯格zeta函数的行列式在变形下的行为。本研究是在几何的一般领域,特别是在双曲n维空间上的Kleinian群。该研究对几何和数学物理都具有重要意义。
英文摘要
This research concerns three areas of spectral geometry: (1) spectral geometry, trace formulas, and determinants for Kleinian groups, (2) finiteness and compactness theorems for isopectral Riemannian manifolds, and (3) spectral geometry of free boundary problems. The research concerns the development of trace formulas and the study of determinants of Laplacians for arbitrary geometrically finite discrete groups of hyperbolic isometries. The emphasis is on co-infinite volume groups, and the goal is to understand poles of the scattering operator geometrically and to study the behavior of the determinant of the Laplacian and Selberg zeta function under deformations. This research is in the general area of geometry and, in particular, Kleinian groups acting on hyperbolic n-dimensional space. The research has significance both to geometry and to mathematical physics.
期刊论文(0)
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会议论文
Conference and Workshop: Scattering and Inverse-Scattering in Multi-Dimensions, May 16-23, 2014
Inverse Scattering and Partial Differential Equations
CBMS Regional Conference in the Mathematical Sciences - Global Harmonic Analysis - June 2011
Spectral Problems in Geometry and Partial Differential Equations
国内基金
海外基金
Handbook of the Mathematics of the Arts and Sciences的中文翻译
  • 批准号:
    12226504
  • 项目类别:
    数学天元基金项目
  • 资助金额:
    20.0万元
  • 批准年份:
    2022
  • 负责人:
    黄朝凌
  • 依托单位:
SCIENCE CHINA: Earth Sciences
Journal of Environmental Sciences
SCIENCE CHINA Information Sciences