We prove that given two metrics g(+) and g(-) with curvature kappa < -1 on a closed, oriented surface S of genus tau >= 2, there exists an AdS(3) 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 AdS(3), we obtain an equivalent result about the prescription of the third fundamental form. This answers partially Question 3.5 in [1].
Prescribing metrics on the boundary of anti-de Sitter 3-manifolds
Tamburelli, Andrea
Primo
2016-01-01
Abstract
We prove that given two metrics g(+) and g(-) with curvature kappa < -1 on a closed, oriented surface S of genus tau >= 2, there exists an AdS(3) 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 AdS(3), we obtain an equivalent result about the prescription of the third fundamental form. This answers partially Question 3.5 in [1].File in questo prodotto:
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