On the filling radius of positively curved Alexandrov spaces (Q1936618)
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scientific article; zbMATH DE number 6134697
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the filling radius of positively curved Alexandrov spaces |
scientific article; zbMATH DE number 6134697 |
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On the filling radius of positively curved Alexandrov spaces (English)
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6 February 2013
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The notion of filling radius was introduced in [\textit{M. Gromov}, J. Differ. Geom. 18, 1--147 (1983; Zbl 0515.53037)]. In the paper under review, the author proves that if a positively curved closed Alexandrov space \(X\) is not isometric to the round sphere, then the filling radius of \(X\) is less than the round sphere's filling radius. This result generalizes the theorem of \textit{F. H. Wilhelm jun.} [Invent. Math. 107, No. 3, 653--668 (1992; Zbl 0729.53044)] for positively curved Riemannian manifolds.
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Alexandrov space
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filling radius
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packing radius
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positively curved
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