TITLE

On the structure of conformally compact Einstein metrics

AUTHOR(S)
Anderson, Michael T.
PUB. DATE
November 2010
SOURCE
Calculus of Variations & Partial Differential Equations;Nov2010, Vol. 39 Issue 3/4, p459
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Let M be an ( n + 1)-dimensional manifold with non-empty boundary, satisfying π( M, ∂ M) = 0. The main result of this paper is that the space of conformally compact Einstein metrics on M is a smooth, infinite dimensional Banach manifold, provided it is non-empty. We also prove full boundary regularity for such metrics in dimension 4 and a local existence and uniqueness theorem for such metrics with prescribed metric and stress-energy tensor at conformal infinity, again in dimension 4. This result also holds for Lorentzian-Einstein metrics with a positive cosmological constant.
ACCESSION #
54354945

 

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