论文标题
Minkowski空间的全球非线性稳定性用于间距类型的初始数据
Global nonlinear stability of Minkowski space for spacelike-characteristic initial data
论文作者
论文摘要
在本文中，我们证明了Minkowski空间在Einstein真空方程的空间类型Cauchy问题的背景下的全球非线性稳定性。空间类型的初始数据位于紧凑的3盘上，未来从其边界发出的完整的零超脸。我们的结果扩展了Christodoulou和Klainerman证明的Minkowski空间的开创性稳定性结果，在该空间上为此开了最初的数据，以3平面的间距类似。 证明依赖于Christodoulou-Klainerman的经典矢量法和引导论证。主要的新颖性是对适合空间类型环境的新几何结构的引入和控制。特别是，它具有带有规定的顶点的空锥，带有规定边界的空间最大超曲面以及Riemannian 3盘上的全球谐波坐标。
In this paper, we prove the global nonlinear stability of Minkowski space in the context of the spacelike-characteristic Cauchy problem for Einstein vacuum equations. Spacelike-characteristic initial data are posed on a compact 3-disk and on the future complete null hypersurface emanating from its boundary. Our result extends the seminal stability result for Minkowski space proved by Christodoulou and Klainerman for which initial data are prescribed on a spacelike 3-plane. The proof relies on the classical vectorfield method and bootstrapping argument from Christodoulou-Klainerman. The main novelty is the introduction and control of new geometric constructions adapted to the spacelike-characteristic setting. In particular, it features null cones with prescribed vertices, spacelike maximal hypersurfaces with prescribed boundaries and global harmonic coordinates on Riemannian 3-disks.
