On the Behavior of Solutions of Einstein

伊森伯格教授将继续一项研究计划，主要集中在爱因斯坦方程的宇宙学解的行为研究上。 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，爱因斯坦场方程在奇异区域附近以及渐近扩展区域附近的解的长期存在性和行为的研究，以及柯西视界时空的研究。 该研究项目还包括其他基于几何的偏微分方程的分析，包括Ricci流和波图。 爱因斯坦的场方程，除了在天体物理学和宇宙学的尺度上提供了引力物理学行为的最好的描述之外，也是一系列数学上有趣的问题的来源。 该项目寻求支持的研究计划，其中重点是其中一些。 这项工作的部分目的是增加数学和理论物理中思想和工具的相互作用。

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.