Planar sections of convex bodies and universal fibrations (Q1781313)
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scientific article; zbMATH DE number 2182772
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Planar sections of convex bodies and universal fibrations |
scientific article; zbMATH DE number 2182772 |
Statements
Planar sections of convex bodies and universal fibrations (English)
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23 June 2005
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A conjecture on tautological vector bundles over Grassmannians, which generalizes the well-known Dvoretsky theorem, is stated and discussed. Moreover it is demonstrated that each three-dimensional real normed space contains a two-dimensional subspace with Banach-Mazur distance from the Euclidean plane at most \(\frac{1}{2}\log \frac{3}{4}\) and this estimate is sharp.
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convex body
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planar section
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affine diameter
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