Abstract:
In this talk we outline recent progress, in joint work with Jim
Isenberg and Rafe Mazzeo, in the development and applications of gluing
constructions for the Einstein Constraint equations within the setting of
the conformal method. We give a description of previous work for constant
mean curvature slices (see gr-qc/0109045, to appear in Comm. Math.
Physics) as well as a recent extension of these results to situations
where the mean curvature is not necessarily constant (see gr-qc/0206034).
Applications of the latter include showing that there are no obstructions
to the topology of asymptotically flat vacuum solutions as well as the
existence of vacuum spacetimes with no maximal Cauchy surfaces.
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Pollack's lecture
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Copyright 29.VIII.02 by P.T.Chrusciel, A.Chopin, and D.Pollack