The Busemann–Petty problem in the complex hyperbolic space
| Autor: | Susanna Dann |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Mathematical Proceedings of the Cambridge Philosophical Society. 155:155-172 |
| ISSN: | 1469-8064 0305-0041 |
| DOI: | 10.1017/s0305004113000054 |
| Popis: | The Busemann–Petty problem asks whether origin-symmetric convex bodies in ℝn with smaller central hyperplane sections necessarily have smaller volume. The answer is affirmative if n ≤ 4 and negative if n ≥ 5. We study this problem in the complex hyperbolic n-space ℍnℂ and prove that the answer is affirmative for n ≤ 2 and negative for n ≥ 3. |
| Databáze: | OpenAIRE |
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