论文标题
渐近平面$ 3 $ 3 $ - 具有边界的manifolds
Mass of asymptotically flat $3$-manifolds with boundary
论文作者
论文摘要
我们使用Bray-Kazaras-Khuri-sern的方法研究了与边界的渐近平坦$ 3 $ manifolds的质量。更确切地说，我们在渐近平坦的歧管和填充边界的结合上得出了一个质量公式，并提供了新的条件，以保证质量的阳性。这种考虑的动机来自研究边界表面的准局部质量。如果边界等法嵌入欧几里得空间中，我们将应用公式沿着大型表面趋于$ \ infty $的棕色质量质量的收敛，其中包括任何固定坐标凸面表面的缩放。
We study the mass of asymptotically flat $3$-manifolds with boundary using the method of Bray-Kazaras-Khuri-Stern. More precisely, we derive a mass formula on the union of an asymptotically flat manifold and fill-ins of its boundary, and give new sufficient conditions guaranteeing the positivity of the mass. Motivation to such consideration comes from studying the quasi-local mass of the boundary surface. If the boundary isometrically embeds in the Euclidean space, we apply the formula to obtain convergence of the Brown-York mass along large surfaces tending to $\infty$ which include the scaling of any fixed coordinate-convex surface.
