Mathematical Sciences: Three-Dimensional Hyperbolic Geometry

数学科学：三维双曲几何

• 批准号: 9102077
• 负责人: Steven Kerckhoff
• 金额: $ 11.47万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-15 至 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102077&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Three; Dimensional; Hyperbolic

The purpose of this project is to analyze various aspects of hyperbolic structures on 3-dimensional manifolds. Professor Kerckhoff will study the deformation theory of hyperbolic cone manifolds, manifolds with Dehn surgery singularities, and infinite-volume geometrically finite manifolds, using a differential geometric analysis of the relevant Hodge theory. Professor Canary wishes to study the analytic and topological structure of the ends of hyperbolic 3-manifolds and their relation to the deformation theory of Kleinian groups. Three-manifolds are very natural objects of study. We live in one, after all. It is therefore surprising what large gaps remain in our knowledge of them.

本项目的目的是分析 三维流形上的双曲结构 教授 Kerckhoff将研究双曲锥的变形理论 流形，具有Dehn手术奇点的流形，以及 无限体积几何有限流形，使用 微分几何分析的相关霍奇理论。 金丝雀教授希望研究的分析和拓扑 双曲三维流形端点的结构及其 与Kleinian群的变形理论有关。 三维流形是非常自然的研究对象。 我们生活 在一个，毕竟。 令人惊讶的是， 我们对他们的了解。