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.

该项目的目的是分析三维流形上双曲结构的各个方面。 Kerckhoff教授将使用相关的Hodge理论的不同几何分析，研究双曲线锥歧管的变形理论，具有Dehn手术奇异性的歧管，具有Dehn手术奇异性的歧管和无限体积的几何歧管。 Canary教授希望研究双曲线3个体的末端的分析和拓扑结构，及其与克莱恩群体变形理论的关系。 三个manifords是非常自然的研究对象。 毕竟，我们生活在一个。 因此，令人惊讶的是，我们对它们的了解中仍然存在什么差距。