标题： 具有近欧几里得边界数据的新渐近平坦静态真空度规 显示英文标题

标题： New asymptotically flat static vacuum metrics with near Euclidean boundary data

摘要： 在我们之前关于近欧几里得边界数据的Bartnik静态真空扩展猜想的工作中，我们建立了一个充分条件，称为静态正则性，并确认了大量边界超曲面是静态正则的。 在本说明中，我们进一步改进了这些先前的结果。 具体来说，我们证明了在某一特定一般光滑单侧超曲面族的一个开且稠密子族中的任何超曲面都是静态正则的。 证明使用了一些我们从研究接近任意静态真空度量的边界数据的猜想中获得的新论点。 显示英文摘要

摘要： 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.