Existence of static vacuum extensions with prescribed Bartnik boundary data
نویسندگان
چکیده
We prove the existence and local uniqueness of asymptotically flat, static vacuum metrics with arbitrarily prescribed Bartnik boundary data that are close to induced on any star-shaped hypersurface or a general family perturbed hypersurfaces in Euclidean space. It confirms part extension conjecture for large classes data, metric obtained is geometrically unique neighborhood metric.
منابع مشابه
On the Bartnik Conjecture for the Static Vacuum Einstein Equations
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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ژورنال
عنوان ژورنال: Cambridge journal of mathematics
سال: 2022
ISSN: ['2168-0930', '2168-0949']
DOI: https://doi.org/10.4310/cjm.2022.v10.n1.a1