Some Problems in Riemannian Geometry

黎曼几何中的一些问题

• 批准号: 0805928
• 负责人: Xiaochun Rong
• 金额: $ 10.2万
• 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: 2008
• 资助国家: 美国
• 起止时间: 2008-06-15 至 2011-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0805928&HistoricalAwards=false
• 关键词: Some; Problems; Riemannian; Geometry

The PI (principal investigator) plans to continue his researchprogram in metric and comparison geometry. The PI is pursuing to solve ormake progress on some basic problems in the following two areas: collapsedRiemannian manifolds with curvature bounded from below and positivelycurved manifolds with symmetry. In this research, mathematics from severaldisciplines interact, such as metric comparison geometry includingAlexandrov geometry, geometric analysis and topology. This project is buiton the early success by PI in the study of the collapsed Riemannianmanifolds with curvature bounded from above and below.Mathematics is the foundation of the natural sciences, anddifferential geometry and Riemannian geometry are among the most importantbranches that interact with other natural sciences such as physics. The PIis pursuing to solve some basic problems in the above fields, which will have a broad intellectual impact. The PI will continue to actively pursue collaborations with other mathematicians in the United States and abroad, and speak at several national and international conferences in the next three years.

PI（首席研究员）计划继续他的研究计划在度量和比较几何。PI致力于解决以下两个领域的一些基本问题或取得进展：曲率有界的黎曼流形和对称的正曲流形。在本研究中，数学的多学科交叉，如度量比较几何（包括亚历山德罗夫几何）、几何分析和拓扑学。这个项目是建立在PI在研究曲率上下有界的坍缩黎曼流形的早期成功之上的。数学是自然科学的基础，微分几何和黎曼几何是与物理学等其他自然科学相互作用的最重要的分支之一。本研究所致力于解决上述领域的一些基本问题，将产生广泛的学术影响。PI将继续积极寻求与美国和国外其他数学家的合作，并在未来三年内在多个国家和国际会议上发言。