Einstein metrics with prescribed conformal infinity on 4-manifolds

Details Einstein metrics with prescribed conformal infinity on 4-manifolds Einstein metrics with prescribed conformal infinity on 4-manifolds

2001-05-29

arxiv.org/abs/math/0105243v5

Mathematics

Differential Geometry

(finally) final version, to appear in GAFA

Scientific paper

This paper considers the existence of conformally compact Einstein metrics on 4-manifolds. A reasonably complete understanding is obtained for the existence of such metrics with prescribed conformal infinity, when the conformal infinity is of positive scalar curvature. We find in particular that general solvability in this class depends on the topology of the filling manifold. The obstruction to solvability for arbitrary boundary values is also identified. While most of the paper concerns dimension 4, some general results on the structure of the space of such metrics hold in all dimensions.

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