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The Busemann–Petty problem in the complex hyperbolic space
Published online by Cambridge University Press: 12 February 2013
Abstract
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.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 1 , July 2013 , pp. 155 - 172
- Copyright
- Copyright © Cambridge Philosophical Society 2013
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