论文标题
双曲线空间中非紧凑型静态结构域通过正质量定理的刚性
Rigidity of non-compact static domains in hyperbolic space via positive mass theorems
论文作者
论文摘要
我们挑出一个静态概念，该概念适用于双曲线空间中的任何域，其边界是一个完全脐带的超出表面。对于（时间对称的）初始数据集，以无穷大为模型的任何一个示例，我们在自然优势能量条件下（无论是内部和边界）中的旋转类别中的正质定理而证明，刚性的刚性较高的效果较低的效果较低的效果，该效果较低，因此稳固的效果均构成了一定的效果。我们方法中的一个关键因素是考虑旋转器和MIT袋边界条件之间插值的椭圆形边界条件家族。
We single out a notion of staticity which applies to any domain in hyperbolic space whose boundary is a non-compact totally umbilical hypersurface. For (time-symmetric) initial data sets modeled at infinity on any of these latter examples, we formulate and prove a positive mass theorem in the spin category under natural dominant energy conditions (both in the interior and along the boundary) whose rigidity statement retrieves, among other things, a sharper version of a recent result by Souam to the effect that no such hypersurface admits a compactly supported deformation keeping the original lower bound on the mean curvature. A key ingredient in our approach is the consideration of a family of elliptic boundary conditions on spinors interpolating between chirality and MIT bag boundary conditions.
