论文标题
稳定的表面和自由边界边缘略微捕获的表面
Stable Surfaces and Free Boundary Marginally Outer Trapped Surfaces
论文作者
论文摘要
我们探索了嵌入式表面的各种稳定性概念，并沉浸在空间和初始数据集中。对这种表面的兴趣在于它们超出了经常是对最小和CMC表面研究的基础的变异技术的潜力。我们证明了$ \ mathbf {h} $的Christodoulou-yau估计值的两个版本 - 稳定的表面，Cohn-vossen类型的不平等现象，用于非紧密稳定稳定的边缘外部捕获的表面（MOTS），以及$ \ Mathbf {H} $ - 稳定稳定的拓扑结构。此外，我们给出了具有边界的MOT的毛细管稳定性的定义。这种稳定的概念导致区域不等式和自由边界稳定MOT的局部分裂定理。最后，我们建立了自由边界MOT的索引估计值和直径估计。这些分别是对自由边界最小表面的Chen-Fraser-Pang和Carlotto-Franz结果的直接概括。
We explore various notions of stability for surfaces embedded and immersed in spacetimes and initial data sets. The interest in such surfaces lies in their potential to go beyond the variational techniques which often underlie the study of minimal and CMC surfaces. We prove two versions of Christodoulou-Yau estimate for $\mathbf{H}$-stable surfaces, a Cohn-Vossen type inequality for non-compact stable marginally outer trapped surface (MOTS), and a global theorem on the topology of $\mathbf{H}$-stable surfaces. Moreover, we give a definition of capillary stability for MOTS with boundary. This notion of stability leads to an area inequality and a local splitting theorem for free boundary stable MOTS. Finally, we establish an index estimate and a diameter estimate for free boundary MOTS. These are straightforward generalizations of Chen-Fraser-Pang and Carlotto-Franz results for free boundary minimal surfaces, respectively.
