Existence of least area planes in hyperbolic 3-space with co-compact metric. (Q1430399)
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scientific article; zbMATH DE number 2069743
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of least area planes in hyperbolic 3-space with co-compact metric. |
scientific article; zbMATH DE number 2069743 |
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Existence of least area planes in hyperbolic 3-space with co-compact metric. (English)
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27 May 2004
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Let \(r\) be a metric on the hyperbolic 3-space \(\mathbb{H}^3\) induced from an arbitrary Riemannian metric on a closed hyperbolic 3-manifold. It is shown that any smooth simple loop in \(S^2_\infty\) spans a properly embedded \(r\)-least area plane in \(\mathbb{H}^3\). This solves \textit{D. Gabai's} conjecture [J. Am. Math. Soc. 10, No. 1, 37--74 (1997; Zbl 0870.57014), Conjecture 3.12], affirmatively.
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Hyperbolic 3-space
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Least area plane
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\(D^2\)-limit lamination
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