On the Bartnik Conjecture for the Static Vacuum Einstein Equations
نویسنده
چکیده
We prove that given any smooth metric γ and smooth positive function H on S, there is a constant λ > 0, depending on (γ,H), and an asymptotically flat solution (M, g, u) of the static vacuum Einstein equations on M = R \ B, such that the induced metric and mean curvature of (M, g, u) at ∂M are given by (γ, λH). This gives a partial resolution of a conjecture of Bartnik.
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