An estimation of the perimeter of a geodesic triangle on a strictly convex surface (Q2746882)
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scientific article; zbMATH DE number 1656816
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An estimation of the perimeter of a geodesic triangle on a strictly convex surface |
scientific article; zbMATH DE number 1656816 |
Statements
11 October 2001
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geodesically convex domain
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Toponogov comparison theorem
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0.90567195
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0.87964034
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0.87944335
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An estimation of the perimeter of a geodesic triangle on a strictly convex surface (English)
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A curve \(\gamma\) on a surface \(M\) of positive curvature is said to be a generalized triangle if 1) \(\gamma\) divides \(M\) into two simply-connected domains and 2) \(\gamma\) consists of three geodesics. The author shows that if \(M\) is a closed convex surface with Gaussian curvature \(K\geq 1\) then the perimeter of every generalized triangle on \(M\) is greater than or equal to \(4\pi\).
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