Prescribing Metrics on the Boundary of Ads 3-manifolds
نویسنده
چکیده
We prove that given two metrics g+ and g− with curvature κ < −1 on a closed, oriented surface S of genus τ ≥ 2, there exists an AdS manifold N with smooth, space-like, strictly convex boundary such that the induced metrics on the two connected components of ∂N are equal to g+ and g−. Using the duality between convex space-like surfaces in AdS3, we obtain an equivalent result about the prescription of the third fundamental form. This answers partially Question 3.5 in [BBD+12].
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Boundary Value Problems for Metrics on 3-manifolds
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