Geometric and Analytic Aspects of Einstein Metrics

爱因斯坦度量的几何和分析方面

• 批准号: 1205947
• 负责人: Michael Anderson
• 金额: $ 31.87万
• 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: 2012
• 资助国家: 美国
• 起止时间: 2012-06-01 至 2016-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1205947&HistoricalAwards=false
• 关键词: Geometric; Analytic; Aspects; Einstein; Metrics

AbstractAward: DMS 1205947, Principal Investigator: Michael T. AndersonThis project concerns several studies in the geometric, analytic and physical aspects of the Einstein equations and applications to related areas. Of particular interest are global issues for boundary value problems for Einstein metrics, including applications to classical differential geometry such as the isometric embedding problem and the study of minimal and constant mean curvature surfaces in space forms. Research will also be carried out on several topics in general relativity, including the study of quasi-local mass and the Bartnik static extension conjecture. Research related to the renormalization group flow in the AdS/CFT correspondence will also be undertaken in a joint project with physicists working in string theory.The Einstein equations have long been a central focus of study and interest to mathematicians and physicists. They are very important on the mathematical side since they are at the forefront of knowledge and research in the areas of geometric analysis and partial differential equations. On the physical side, they govern our understanding of large-scale physics - the formation of stars, galaxies and the structure of the universe as a whole. As a concrete application, GPS would not be possible without a thorough and full understanding of the Einstein equations. In addition, they lie at the core of string theory - the most actively studied subject in high energy theoretical physics. The project will involve collaboration and interaction between mathematicians and physicists seeking to unravel some of the mysteries of these equations. In addition, the project involves the training of graduate students in these areas important for the future of basic research.

Abstractaward：DMS 1205947，主要研究人员：Michael T. Andersonthis项目涉及爱因斯坦方程的几何，分析和物理方面的几项研究，以及对相关领域的应用。特别感兴趣的是爱因斯坦指标边界价值问题的全球问题，包括应用于经典差异几何形状，例如等距嵌入问题以及对空间形式中最小和恒定平均曲率表面的研究。研究还将在一般相对论中进行几个主题，包括研究准局部质量和Bartnik静态扩展猜想。与弦理论的物理学家的联合项目，与ADS/CFT对应中的重新归一化组流有关的研究也将进行。爱因斯坦方程一直是数学家和物理学家的研究和兴趣的核心重点。它们在数学方面非常重要，因为它们在几何分析和部分微分方程领域处于知识和研究的最前沿。在物理方面，它们控制着我们对大规模物理学的理解 - 星系，星系和整个宇宙的结构。作为一种具体的应用，如果没有对爱因斯坦方程的全面和充分的理解，则不可能进行全科医生。此外，它们是弦理论的核心 - 高能量理论物理学中最积极的学科。 该项目将涉及数学家与寻求揭开这些方程式某些奥秘的物理学家之间的合作和互动。此外，该项目涉及对这些领域的研究生的培训，对基础研究的未来很重要。