Random \(k\)-surfaces (Q2388269)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Random \(k\)-surfaces |
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Random \(k\)-surfaces (English)
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12 September 2005
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Let \(N\) be a compact manifold, with curvature less than \(-1\). Surfaces of dimension two immersed into \(N\) whose product of principal curvatures equals a constant \(k\in\left( 0;1\right)\) are called \(k\)-surfaces. The author constructs the space of pointed \(k\)-surfaces and proves that this space admits infinitely many mutually singular, ergodic transverse finite measures of full support.
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negatively curved Riemannian manifold
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2-dimensional surface
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principal curvatures
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2-dimensional lamination
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invariant measure
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