On Boundary Value Problems for Einstein Metrics
نویسنده
چکیده
On any given compact manifold M with boundary ∂M , it is proved that the moduli space E of Einstein metrics on M , if non-empty, is a smooth, infinite dimensional Banach manifold, at least when π1(M,∂M) = 0. Thus, the Einstein moduli space is unobstructed. The usual Dirichlet and Neumann boundary maps to data on ∂M are smooth, but not Fredholm. Instead, one has natural mixed boundary-value problems which give Fredholm boundary maps. These results also hold for manifolds with compact boundary which have a finite number of locally asymtotically flat ends, as well as for the Einstein equations coupled to many other fields.
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