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The Busemann–Petty problem in the complex hyperbolic space

Published online by Cambridge University Press:  12 February 2013

SUSANNA DANN
SUSANNA DANN*
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A. e-mail: danns@missouri.edu
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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.

Type
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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