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

Isenberg教授的研究主要涉及两个领域：(1)满足爱因斯坦方程的时空中引力场的动力学及其在奇点附近的行为；(2)三维流形上Reimannian度规的Ricci流的收敛和不收敛。虽然对第一个领域的兴趣来自物理，而对第二个领域的兴趣来自数学，但在这两个领域，分析都集中在基于几何的偏微分方程组。此外，在这两个问题中，最紧迫(也是最困难的)问题涉及解决方案的长期行为，以及当它们变得单一时领域的行为。因此，不足为奇的是，这两个领域取得的进展往往建立在使用一些类似工具的基础上。同样不令人惊讶的是，在研究这两个问题时使用的物理动机的想法和基于数学的概念之间发生了相当大的交叉。

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.