论文标题
带有规定的Bartnik边界数据附近的静态真空扩展，靠近一般静态真空度量
Static vacuum extensions with prescribed Bartnik boundary data near a general static vacuum metric
论文作者
论文摘要
我们介绍了（i）类型和（ii）类型的静态常规概念，并表明它们是局部适当的条件，可以用规定的bartnik边界数据求解渐近平坦的静态真空度量。然后，我们表明，在非常普遍的开放和密集的Hypersurfaces家族中的高度曲面是（II）类型的静态常规。作为应用，我们证实了Bartnik的静态真空扩展猜想，用于大量的Bartnik边界数据，包括那些可以远离欧几里得和具有较大ADM群众的静态真空延伸，并提供许多具有吸引人几何形状的静态真空度量的新示例。
We introduce the notions of static regular of type (I) and type (II) and show that they are sufficient conditions for local well-posedness of solving asymptotically flat, static vacuum metrics with prescribed Bartnik boundary data. We then show that hypersurfaces in a very general open and dense family of hypersurfaces are static regular of type (II). As applications, we confirm Bartnik's static vacuum extension conjecture for a large class of Bartnik boundary data, including those that can be far from Euclidean and have large ADM masses, and give many new examples of static vacuum metrics with intriguing geometry.
