具有给定 Bartnik 边界数据的静态真空延拓的存在性
微分几何
2022-03-03 v4 广义相对论与量子宇宙学
摘要
我们证明了渐近平坦、静态真空度量的存在性与局部唯一性，其任意给定的 Bartnik 边界数据接近于欧几里得空间中任意星型超曲面或一般扰动超曲面族上的诱导边界数据。这证实了 Bartnik 静态延拓猜想在大量边界数据类上的存在性部分，且所得静态真空度量在欧几里得度量邻域内几何唯一。
关键词
引用
@article{arxiv.2103.15887,
title = {Existence of static vacuum extensions with prescribed Bartnik boundary data},
author = {Zhongshan An and Lan-Hsuan Huang},
journal= {arXiv preprint arXiv:2103.15887},
year = {2022}
}
备注
In Version 2, Lemma 4.8 is strengthened. In Version 3, Corollary 8 strengthened to include star-shaped hypersurfaces. We are very grateful to Pengzi Miao for pointing it out. Version 4 matched the version to appear in Cambridge Journal of Mathematics