Abstract.
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 depends on the topology of the filling manifold. The obstruction to extending these results to 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.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Partially supported by NSF Grant DMS 0604735.
Received: April 2006, Revision: November 2006, Accepted: February 2008
Rights and permissions
About this article
Cite this article
Anderson, M.T. Einstein Metrics with Prescribed Conformal Infinity on 4-Manifolds. GAFA Geom. funct. anal. 18, 305–366 (2008). https://doi.org/10.1007/s00039-008-0668-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00039-008-0668-5