Closedness of the Space of Ahe Metrics on 4-manifolds
نویسنده
چکیده
Let M be a compact 4-manifold with boundary ∂M , and consider the moduli space EAH of asymptotically hyperbolic Einstein (AHE) metrics on M . Any such metric g induces a conformal class [γ] of metrics on ∂M , called the conformal infinity of g. In this paper, we prove that the space of boundary values BAH of metrics in EAH is closed under natural conditions, i.e. if [γi] is a sequence of conformal infinities of AHE metrics gi and [γi] → [γ], then {gi} converges to an AHE metric g with conformal infinity [γ]. In addition, we prove some results on the boundary regularity of AHE metrics on 4-manifolds.
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