On the Behavior of Solutions of Einstein's Equations and Other Geometric Nonlinear Partial Differential Equation Systems

关于爱因斯坦方程和其他几何非线性偏微分方程组解的行为

• 批准号: 0968612
• 负责人: James Isenberg
• 金额: $ 33万
• 依托单位: University of Oregon Eugene
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0968612&HistoricalAwards=false
• 关键词: Behavior; Solutions; Einstein; Equations; Other

As the observational evidence supporting Einstein's theory of general relativity as the pre-eminent model for the gravitational field in astrophysics and cosmology grows stronger, it becomes increasingly important to use the latest mathematical tools to carefully explore the implications of the theory. This award supports a focus on new procedures for constructing spacetimes representing the the interaction of many bodies, and also on new techniques which allow us to probe the nature of the cosmological singularities predicted by Einstein's theory.This award also supports work which studies various aspects of Ricci flow, the analytical tool which has proven to be spectacularly successful in proving the Poincare Conjecture and the Geometrization Conjecture in three dimensions. There is much work to do in understanding the details of the dynamics of Ricci flow, and how it might be used to further analyze the relationship between geometry and topology, and this proposal supports such work, including a number of studies of Ricci flow stability.A graduate student will participate in the supported research as part of a PhD dissertation.

随着观测证据支持爱因斯坦的广义相对论作为天体物理学和宇宙学中引力场的卓越模型变得越来越强大，使用最新的数学工具仔细探索该理论的含义变得越来越重要。该奖项支持对构建时空的新程序的关注，这些新程序代表了许多物体的相互作用，也支持对新技术的关注，这些新技术使我们能够探索爱因斯坦理论所预测的宇宙学奇点的性质。该奖项还支持研究里奇流的各个方面的工作，该分析工具已被证明是非常成功的证明庞加莱猜想和几何化猜想在三维空间。在理解Ricci流的动力学细节方面还有很多工作要做，以及如何使用它来进一步分析几何和拓扑之间的关系，这个建议支持这样的工作，包括一些Ricci流稳定性的研究。