On convexity of hypersurfaces in the hyperbolic space |
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Authors: | Konstantin Rybnikov |
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Institution: | (1) University of Massachusetts at Lowell, One University Ave., Lowell, MA 01854, USA |
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Abstract: | In the Hyperbolic space \({\mathbb{H}^n}\) (n ≥ 3) there are uncountably many topological types of convex hypersurfaces. When is a locally convex hypersurface in \({\mathbb{H}^n}\) globally convex, that is, when does it bound a convex set? We prove that any locally convex proper embedding of an (n ? 1)-dimensional connected manifold is the boundary of a convex set whenever the complement of (n ? 1)-flats of the resulting hypersurface is connected. |
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Keywords: | Hyperbolic Convex Local convexity Hypersurface |
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