The asymptotic boundary of a surface imbedded in \(H^ 3\) with nonnegative curvature (Q579644)
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scientific article; zbMATH DE number 4015637
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The asymptotic boundary of a surface imbedded in \(H^ 3\) with nonnegative curvature |
scientific article; zbMATH DE number 4015637 |
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The asymptotic boundary of a surface imbedded in \(H^ 3\) with nonnegative curvature (English)
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1987
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The main result of this paper is that the asymptotic boundary of an imbedding of \({\mathbb{R}}^ 2\) with non-negative Gauss curvature into \(H^ 3\) is a single point. It is also proved that a surface in \(H^ 3\) that is locally strictly convex and has one point in its asymptotic boundary is the boundary of a convex body and homeomorphic to \({\mathbb{R}}^ 2\).
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asymptotic boundary
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non-negative Gauss curvature
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boundary of a convex body
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