论文标题
具有近乎欧几里得边界数据的新的渐近平坦静态真空指标
New asymptotically flat static vacuum metrics with near Euclidean boundary data
论文作者
论文摘要
在我们对Bartnik的静态真空扩展的先前工作中，对于近乎欧几里得边界数据，我们建立了一个足够的条件，称为静态常规，并确认大量的边界悬浮面是静态的。在本说明中，我们进一步改善了一些先前的结果。具体而言，我们表明，在特定一般光滑的单侧超曲面家族（不一定是叶子）的开放式亚家族中的任何超表面都是静态的。该证明使用了我们的一些新论点，这是由于研究任意静态真空度量的边界数据的猜想而动机。
In our prior work toward Bartnik's static vacuum extension conjecture for near Euclidean boundary data, we establish a sufficient condition, called static regular, and confirm large classes of boundary hypersurfaces are static regular. In this note, we further improve some of those prior results. Specifically, we show that any hypersurface in an open and dense subfamily of a certain general smooth one-sided family of hypersurfaces (not necessarily a foliation) is static regular. The proof uses some of our new arguments motivated from studying the conjecture for boundary data near an arbitrary static vacuum metric.
