标题： 边缘外陷阱表面与毛细边界及初始数据集的刚性 显示英文标题

标题： Marginally outer trap surface with capillary boundary and rigidity of initial data sets

摘要： 在本文中，我们提出了当一个具有毛细边界的小外陷阱面（MOTS）被嵌入时，带有边界的初始数据集的几个刚性结果。 首先，我们建立了具有毛细边界的小外陷阱面的面积估计。 接下来，我们证明了带有边界的三维初始数据集的刚性结果。 此外，我们使用Yamabe常数将我们的结果从三维情况扩展到高维初始数据集。 显示英文摘要

摘要： In this paper, we present the several rigidity results of initial data sets with boundary when a marginally outer trap surface (MOTS) with capillary boundary is embedded. First, we establish estimates for the area of a MOTS with capillary boundary. Next, we prove a rigidity for 3-dimensional initial data sets with boundary. Furthermore, we extend our results from the 3-dimensional case to the high dimensional initial data sets using the Yamabe constant.