Mathematical Sciences: Some Spectral and Isospectral Problems in Riemannian Geometry

数学科学：黎曼几何中的一些谱和等谱问题

• 批准号: 9006092
• 负责人: Peter Perry
• 金额: $ 4.26万
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9006092&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Spectral; Isospectral

The principal investigator will continue his research in two areas of spectral geometry. The first involves isospectral three dimensional manifolds with curvature assumptions but no restriction on conformal class. In the second project he will develop a trace formula and Selberg zeta function for arbitrary geometrically finite discrete groups whose fundamental regions have infinite hyperbolic volume. The principal investigator will extend his theories of isospectral manifolds which are not necessarily isometric. In two dimensions, isospectral manifolds are surfaces which sound alike when struck. In higher dimensions, examples are known of hypersurfaces which sound alike but which are not isometric; that is, they do not have identical shapes.

首席研究员将继续他的研究在两个 光谱几何学领域。 第一个涉及等光谱三 有曲率假设但没有 保形类的限制。 在第二个项目中， 建立了任意函数的迹公式和Selberg zeta函数， 几何有限离散群， 有无穷大的双曲体积 首席研究员将扩展他的理论， 不一定等距的等谱流形。 在 二维等谱流形是一种表面， 被击中时也一样。 在更高的维度中，已知的例子是 听起来相似但不是等距的超曲面; 它们的形状不一样