Mathematical Sciences: Mathematical Studies of Gravity and Other Fields in Spacetime

数学科学：引力和时空中其他场的数学研究

• 批准号: 8706494
• 负责人: James Isenberg
• 金额: $ 3.1万
• 依托单位: University of Oregon Eugene
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-01 至 1989-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8706494&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Gravity; Other

James Isenberg will apply the methods of modern geometrical analysis to examine certain questions arising in the study of gravitational and other fields in spacetime. The techniques to be applied will arise from Lie group theory, symplectic geometry, algebraic geometry, and the theory of elliptic and hyperbolic partial differential equations. Amongst the questions to be studied are 1) Is it true that all spacetimes which satisfy Einstein's equations and are extendible across a compact Cauchy horizon must contain Killing vector fields? 2) Can the class of spatially homogeneous solutions of the Einstein Yang-Mills equations be treated as a finite dimensional dynamical system? 3) Can the behavior of constant mean curvature surfaces or hypersurfaces be systematically analyzed near singular regions in the ambient manifold?

詹姆斯·伊森伯格将运用现代几何学的方法 分析研究中出现的某些问题 引力场和其他时空场这些技术 应用将来自李群理论，辛几何， 代数几何，椭圆和双曲理论 偏微分方程 要研究的问题包括：（1） 所有满足爱因斯坦方程的时空 在紧柯西视界上可拓的 向量场2)空间齐次类 Einstein Yang-Mills方程的解被视为一个 有限维动力系统3)的行为是否 常平均曲率曲面或超曲面是 系统地分析了周围环境中的近奇异区域， 歧管？