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

点击翻译按钮获取中文摘要

Einstein's field equations, besides providing the basis for the best current description of the behavior of gravitational physics on the astrophysical and cosmological scale, also is the source of a rich collection of mathematically interesting questions. Prof. Isenberg will investigate several of these, including: 1. solutions of the Einstein constraint equations of a more general character than currently known 2. occurrence of singularities in solutions to Einstein's equations (i.e. the so-called "Strong Cosmic Censorship" conjecture) 3. the relationship between mathematical manifolds and their geometries (i.e. "Ricci flows") This work will increase the interaction of ideas and tools in mathematics and theoretical physics.