论文标题
爱因斯坦类型系统完全流形
Einstein Type Systems on Complete Manifolds
论文作者
论文摘要
在本文中，我们通过共形方法研究了耦合的爱因斯坦约束方程（ECE），重点是具有灵活的渐近性的非紧凑型歧管。特别是，我们没有施加任何特定模型，以说明有界几何形状的初始数据集的动机，我们将其在物理上被标准的宇宙学空间 - 带有非紧凑型Cauchy hyperfaces的标准宇宙学空间。首先，我们证明了与边界紧凑的歧管上的存在标准，该标准适用于更通用的系统，可以看作是耦合ECE的已知存在理论的自然扩展。在此基础上，我们证明了完整的歧管上的存在标准，具有适当的障碍功能，适用于一个完全动机的耦合系统的全部障碍功能。最后，我们构建障碍功能，从而在有限的几何情况下显示出存在。
In the present paper, we study the coupled Einstein Constraint Equations (ECE) on complete manifolds through the conformal method, focusing on non-compact manifolds with flexible asymptotics. In particular, we do not impose any specific model for infinity being motivated to account for initial data sets of bounded geometry, which we take to be physically well motivated by standard cosmological space-times with non-compact Cauchy hypersurfaces. First, we prove an existence criteria on compact manifolds with boundary which applies to more general systems and can be seen as a natural extension of known existence theory for the coupled ECE. Building on this, we prove an existence criterium on complete manifolds with appropriate barrier functions for a family of physically well-motivated coupled systems on complete manifolds. Finally, we build barrier functions and thus show existence in the bounded geometry case.
