Problems in Metric Riemannian Geometry

公制黎曼几何问题

• 批准号: 1106517
• 负责人: Xiaochun Rong
• 金额: $ 12.69万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-15 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1106517&HistoricalAwards=false
• 关键词: Problems; Metric; Riemannian; Geometry

The principal investigator plans to continue his research in Riemannian metric geometry; in particular some basic problems in two area: (1) collapsed Riemannian manifolds with bounded sectional curvature (in absolute value or from below) and (2) rigidity and stability problems in Alexandrov geometry. In his research, mathematics from several disciplines interact, such as metric Riemannian geometry, analysis and partial differential equations, compact transformation group theory and topology. This project is amplified by the fact that among the manifolds of same dimension whose sectional curvature is bounded from between below and whose diameter is bounded above by a constant, all but finitely many are collapsed and are close to some Alexandrov spaces.Mathematics is the foundation of the natural sciences, and differential geometry/ Riemannian geometry are among the most important branches of mathematics. The PI is pursuing solving some basic problems in this field that would have a broad intellectual impact. The PI will continue to actively pursue collaborations with other mathematicians in the United States and abroad and to speak at several national and international meetings a year.

首席研究员计划继续黎曼度量几何的研究；特别是两个领域的一些基本问题：（1）具有有界截面曲率（绝对值或从下）的折叠黎曼流形和（2）亚历山德罗夫几何中的刚性和稳定性问题。在他的研究中，来自多个学科的数学相互作用，例如度量黎曼几何、分析和偏微分方程、紧变换群理论和拓扑。这个项目被放大的事实是，在截面曲率由下界和直径由常数上界的相同维流形中，除了有限的多个流形之外，所有流形都折叠并接近某些亚历山德罗夫空间。数学是自然科学的基础，微分几何/黎曼几何是数学最重要的分支之一。 PI 致力于解决该领域的一些基本问题，这些问题将产生广泛的智力影响。 PI 将继续积极寻求与美国和国外其他数学家的合作，并每年在几次国内和国际会议上发表演讲。