Связь между объемом и площадью шаров в геометрии Гильберта
We show that the spheres in the Hilbert geometry have the same volume growth rate as those in the Lobachevsky space. We give the asymptotic estimates for the ratio of the volume of a metric ball to the area of a metric sphere in the Hilbert geometry. The derived estimates agree with the well-known f...
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| Date: | 2008 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
| Published: |
Видавничий дім "Академперіодика" НАН України
2008
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| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/4964 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Связь между объемом и площадью шаров в геометрии Гильберта / А.А. Борисенко, Е.А. Олин // Доп. НАН України. — 2008. — № 7. — С. 7-9. — Бібліогр.: 5 назв. — рос. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We show that the spheres in the Hilbert geometry have the same volume growth rate as those in the Lobachevsky space. We give the asymptotic estimates for the ratio of the volume of a metric ball to the area of a metric sphere in the Hilbert geometry. The derived estimates agree with the well-known facts for the Lobachevsky space.
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| ISSN: | 1025-6415 |