We establish the charged Penrose inequality$$\begin{aligned} m\ge \frac{1}{2}\left( \rho + \frac{q^2}{\rho } \right) \end{aligned}$$for time-symmetric initial data sets having an outermost minimal surface boundary and finitely many asymptotically cylindrical ends, with an appropriate rigidity statement. This is accomplished by a doubling argument based on the work of Weinstein and Yamada (Commun Math Phys 257:703–723, 2005). arXiv:math/0405602) and a subsequent application of the ordinary charged Penrose inequality as established by Khuri et al. (Contemp Math 653:219–226, 2015. arXiv:1308.3771; J Differ Geom 106:451–498, 2017. arXiv:1409.3271). Furthermore, the techniques used in the aforementioned proof allow for an alternative proof of the positive mass theorem with charge for such manifolds, a result originally obtained in Bartnik and Chrusciel (Journal für die reine und angewandte Mathematik 579:13–73, 2005).

中文翻译：

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具有渐近圆柱端的流形的带电荷的Penrose不等式和正质量定理

我们建立带电的Penrose不等式$$ \ begin {aligned} m \ ge \ frac {1} {2} \ left（\ rho + \ frac {q ^ 2} {\ rho} right）\ end {aligned} $ $对于时间对称的初始数据集，它具有最外面的最小表面边界和有限多个渐近圆柱端，并带有适当的刚度声明。这是通过基于Weinstein和Yamada的工作的加倍论证来实现的（Commun Math Phys 257：703–723，2005）。arXiv：math / 0405602）以及随后由Khuri等人建立的普通带电Penrose不等式的应用。（当代数学653：219-226，2015。arXiv：1308.3771； J Differ Geom 106：451-498，2017。arXiv：1409.3271）。此外，上述证明中使用的技术允许对带有此类流形的正质量定理进行替代证明，这是最初在Bartnik和Chrusciel中获得的结果（Journal rein und angewandte Mathematik 579：13-73，2005）。