Static potentials and area minimizing hypersurfaces
Static potentials and area minimizing hypersurfaces
复制标题
静态势和面积最小化超曲面
DOI：
10.1090/proc/13936
复制
发表时间：
2017
影响因子：
6.4
通讯作者：
P. Miao
中科院分区：
文献类型：
--
作者：
Lan;Daniel Martin;P. Miao
证明了具有视界边界的渐近平坦流形存在全局静态势时，其静态势在边界上必须为零。我们还证明了如果一个具有视界边界的渐近平坦流形在其外部区域允许无界的静态势，则该流形必须包含一个完全的非紧化面积最小化超曲面。得到了有关黎曼正质量定理和巴特尼克准局部质量的一些结果。
We show that if an asymptotically flat manifold with horizon boundary admits a global static potential, then the static potential must be zero on the boundary. We also show that if an asymptotically flat manifold with horizon boundary admits an unbounded static potential in the exterior region, then the manifold must contain a complete non-compact area minimizing hypersurface. Some results related to the Riemannian positive mass theorem and Bartnik's quasi-local mass are obtained.