Total curvature and length estimate for curves in CAT(\(K\)) spaces. (Q1410601)
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scientific article; zbMATH DE number 1992876
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Total curvature and length estimate for curves in CAT(\(K\)) spaces. |
scientific article; zbMATH DE number 1992876 |
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Total curvature and length estimate for curves in CAT(\(K\)) spaces. (English)
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14 October 2003
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The authors study curves \(c\) in metric spaces \(M\) with bounded Alexandrov curvature \(K.\) In each open neighborhood \(U\) of a point there exist estimates for minimizing geodesic triangles with perimeter \(\leq 2 \pi/\sqrt{K}\). The curves are being approximated by a series of minimizing geodesics -- a limit procedure delivers basic properties of the curve \(c\) such as total curvature and estimates for the overall length of \(c\).
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total curvature of curves
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length estimates
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bounded curvature
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