Finite Boundary Regularity for Conformally Compact Einstein Manifolds of Dimension 4
Differential Geometry
2020-05-27 v3
Abstract
We prove that a dimensional conformally compact Einstein manifold with H\"older continuous scalar curvature and with boundary metric has a compactification. We also study the regularity of the new structure and the new defining function. This is a supplementary proof of Anderson's work and an improvement of Helliwell's result in dimension 4.
Keywords
Cite
@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}
}
Comments
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