四维共形紧 Einstein 流形的有限边界正则性
微分几何
2020-05-27 v3
摘要
我们证明，具有 Hölder 连续数量曲率的四维 C^2 共形紧 Einstein 流形，若其边界度量为 C^{m,α}，则具有 C^{m,α} 紧化。我们还研究了新结构与新定义函数的正则性。这是对 Anderson 工作的补充证明，也是对 Helliwell 在四维结果的改进。
引用
@article{arxiv.1911.01885,
title = {Finite Boundary Regularity for Conformally Compact Einstein Manifolds of Dimension 4},
author = {Xiaoshang Jin},
journal= {arXiv preprint arXiv:1911.01885},
year = {2020}
}
备注
22 pages. Changed the proof in page 17 and 18 and removed the condition "and the mean curvature $H\in C^{1,\sigma}(\partial M)$" in Theorem 1.1. Removed and changed some sentences concerning the mean curvature in other places