论文标题
带有环形无穷大的渐近倍曲面初始数据集的正能定理和相关的刚度结果
The Positive Energy Theorem for Asymptotically Hyperboloidal Initial Data Sets With Toroidal Infinity and Related Rigidity Results
论文作者
论文摘要
我们建立了带有环形无穷大，弱捕获的边界并满足主要能量条件的3维倍倍曲折初始数据集的正能定理和Penrose型不等式。在脐带案件中，证明了刚度表明，当初始数据歧管与相关Kottler Spacetime的规范切片的一部分等静电时，总能量完全消失。此外，我们提供了一个新的证据，证明了eichmair-galloway-mendes [10]在维度3中的刚度定理，在某些情况下，假设弱。这些结果是通过分析时空谐波函数的水平集获得的。
We establish the positive energy theorem and a Penrose-type inequality for 3-dimensional asymptotically hyperboloidal initial data sets with toroidal infinity, weakly trapped boundary, and satisfying the dominant energy condition. In the umbilic case, a rigidity statement is proven showing that the total energy vanishes precisely when the initial data manifold is isometric to a portion of the canonical slice of the associated Kottler spacetime. Furthermore, we provide a new proof of the recent rigidity theorems of Eichmair-Galloway-Mendes [10] in dimension 3, with weakened hypotheses in certain cases. These results are obtained through an analysis of the level sets of spacetime harmonic functions.
