Studies on Einstein Metrics and Related Topics

爱因斯坦度量及相关主题的研究

• 批准号: 0072591
• 负责人: Michael Anderson
• 金额: $ 33.82万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072591&HistoricalAwards=false
• 关键词: Studies; Einstein; Metrics; Related; Topics

AbstractAward: DMS-0072591Principal Investigator: Michael T. AndersonAnderson and LeBrun both plan to study the global Riemanniangeometry of low-dimensional manifolds, with an eye towards theramifications of these results for smooth topology, algebraicgeometry, and theoretical physics. Anderson will continue work onThurston's geometrization conjecture, and study relations of thisconjecture with global existence and singularity formation forvacuum space-times in general relativity. LeBrun will studyrelations between properties of the total scalar curvaturefunctional and smooth topology, as well as related problemsconcerning quadratic curvature functionals. In addition,Anderson and LeBrun both plan to investigate topics in thegeometry of asymptotically hyperbolic manifolds, and relationswith current issues in string theory and the AdS/CFTcorrespondence.Anderson's investigations are directly related to questionsregarding the physics of black holes and the shape and long-termevolution of the universe. LeBrun's work studies fundamentalquestions arising from Hawking's quantum gravity program, andrelates the Seiberg-Witten equations of high-energy physics tothe study of gravitational phenomena.

Abstractaward：DMS-0072591原理研究者：Michael T. Andersonanderson和Lebrun都计划研究低维歧管的全球Riemannianianianiangemetry，并着眼于这些结果的疗程，以供这些结果，以实现平滑拓扑结构，代数测定法和理论物理学。安德森（Anderson）将继续工作Onthurston的几何化猜想，并研究该注射器与全球存在和奇异性形成的关系。 LeBrun将研究总标量曲率功能和平滑拓扑的性能，以及相关的问题，即辅助二弯曲功能。 此外，安德森（Anderson）和勒布朗（Lebrun）都计划研究渐近双曲线歧管的几何中的主题，以及与弦理论和ADS/CFTCorresporce中的当前问题的关系。Anderson的研究直接与质疑黑孔的物理和宇宙的形状和长期变化的问题有关。 Lebrun的工作研究是由Hawking的量子重力计划引起的基本问题，它遵循了对引力现象的高能量物理学研究的Seiberg-inten方程。