On the Behavior of Solutions of Einstein

伊森伯格教授将继续一项主要专注于研究爱因斯坦方程宇宙学解的行为的研究计划。利用几何分析和非线性偏微分方程理论的工具，他的研究涉及爱因斯坦约束方程的解的研究，爱因斯坦场方程解在奇异区和近渐近展开区的长时间存在性和性态的研究，以及具有柯西视界的时空的研究。该研究计划还包括分析其他基于几何的偏微分方程式，包括Ricci流动和波图。爱因斯坦的场方程式，除了对引力物理在天体物理和宇宙尺度上的行为提供了最好的当前描述外，也是大量数学有趣问题的来源。这个项目寻求支持一个专注于其中一些的研究计划。这项拟议工作的部分目的是增加数学和理论物理中的思想和工具的互动。

Prof. Isenberg will continue a program of research which focuses primarily on the study of the behavior of cosmological solutions of Einstein's equations. Employing tools from geometrical analysis and nonlinear partial differential equation theory, his research involves the study of solutions of the Einstein constraint equations, the study of long-time existence and behavior of solutions of the Einstein field equations near singular regions as well as near asymptotic expansion regions, and the study of spacetimes with Cauchy horizons. This research program also includes analysis of other geometrically-based partial differential equations, including Ricci flow and wave maps. Einstein's field equations, besides providing the best current description of the behavior of gravitational physics on the astrophysical and cosmological scales, is also the source of a rich collection of mathematically interesting questions. This project seeks support for a program of research which focuses on some of these. Part of the aim of this proposed work is to increase the interaction of ideas and tools in mathematics and theoretical physics.