Zum isodiametrischen Problem im hyperbolischen Raum. (On the isodiametric problem in the hyperbolic space) (Q1102546)
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scientific article; zbMATH DE number 4050427
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Zum isodiametrischen Problem im hyperbolischen Raum. (On the isodiametric problem in the hyperbolic space) |
scientific article; zbMATH DE number 4050427 |
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Zum isodiametrischen Problem im hyperbolischen Raum. (On the isodiametric problem in the hyperbolic space) (English)
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1988
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The author generalizes the concept of Steiner symmetrization to hyperbolic space. The thus generalized symmetrization preserves the volume, maps balls onto balls and does not increase the diameter of a set. The latter property is then used to show that among all compact sets having the same diameter precisely the balls have maximum volume (inequality of Bieberbach).
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Bieberbach inequality
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isodiametric problem
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Steiner symmetrization
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hyperbolic space
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