A comparison theorem on simply connected complete Riemannian manifolds (Q1419642)
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scientific article; zbMATH DE number 2028865
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A comparison theorem on simply connected complete Riemannian manifolds |
scientific article; zbMATH DE number 2028865 |
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A comparison theorem on simply connected complete Riemannian manifolds (English)
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19 January 2004
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Consider a simply connected complete Riemannian manifold with sectional curvature bounded above by \(-1\) and a curve in this space with geodesic curvature bounded by~\(1\) in absolute value. Generalizing a result in hyperbolic geometry, the author shows that this curve approaches the boundary. He estimates how fast this happens via the convergence of an improper integral.
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negative curvature
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Aleksandrov triangles
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