The Journal of Geometric Analysis ( IF 0.924 ) Pub Date : 2020-05-25 , DOI: 10.1007/s12220-020-00423-0
Xiaoshang Jin

We prove that a 4-dimensional $$C^2$$ conformally compact Einstein manifold with Hölder continuous scalar curvature and with $$C^{m,\alpha }$$ boundary metric has a $$C^{m,\alpha }$$ 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.

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