Boundary Regularity for Conformally Compact Einstein Metrics in Even Dimensions

Details Boundary Regularity for Conformally Compact Einstein Metrics in Even Dimensions Boundary Regularity for Conformally Compact Einstein Metrics in Even Dimensions

2007-05-18

arxiv.org/abs/0705.2625v2

Mathematics

Differential Geometry

30 pages, minor typos corrected, content in section 7 clarified, references updated

Scientific paper

We study boundary regularity for conformally compact Einstein metrics in even dimensions by generalizing the ideas of Michael Anderson. Our method of approach is to view the vanishing of the Ambient Obstruction tensor as an nth order system of equations for the components of a compactification of the given metric. This, together with boundary conditions that the compactification is shown to satisfy provide enough information to apply classical boundary regularity results. These results then provide local and global versions of finite boundary regularity for the components of the compactification.

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