On the Behavior of Solutions of Einstein's Equations and the Behavior of Ricci Flows (Physics)

伊森伯格教授的研究主要涉及两个方面 研究领域：（1）引力场的动力学， 它们在时空奇点附近的行为满足 爱因斯坦方程;（2）收敛性和 黎曼度量的Ricci流在三个 维流形 虽然对第一个领域的兴趣 第二个领域是数学， 在这两个方面，分析重点是基于几何的 偏微分方程组 此外，在这两个方面， 最紧迫（和最困难）的问题涉及长期的 解的行为和场的行为， 他们变得单一。 因此，毫不奇怪， 在这两个领域取得的进展往往是基于 使用类似的工具。 同样不足为奇的是， 大量的交叉受精发生在 物理驱动的想法和基于物理的概念 这两个问题的研究都用到了它。

The research of Prof. Isenberg involves primarily two areas of study: (1) The dynamics of gravitational fields and their behavior near singularities in spacetimes satisfying Einstein's equations; and (2) The convergence and nonconvergence of Ricci flows of Reimannian metrics on three- dimensional manifolds. While the interest in the first area comes from physics and that in the second area is mathematical, in both areas the analysis focuses on geometrically-based systems of partial differential equations. Moreover, in both, the most pressing (and difficult) issues involve the long-time behavior of the solutions, and the behavior of the fields as they become singular. Therefore it is not surprising that the progress achieved in the two areas has been often based on the use of somewhat similar tools. Also not surprising is the considerable cross-fertilization which has occurred between the physically-motivated ideas and mathematically-based concepts which are used in studying both problems.