The Busemann–Petty problem in hyperbolic and spherical spaces

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The Busemann-petty Problem in Hyperbolic and Spherical Spaces

The Busemann-Petty problem asks whether origin-symmetric convex bodies in R with smaller central hyperplane sections necessarily have smaller n-dimensional volume. It is known that the answer to this problem is affirmative if n ≤ 4 and negative if n ≥ 5. We study this problem in hyperbolic and spherical spaces.

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ژورنال

عنوان ژورنال: Advances in Mathematics

سال: 2006

ISSN: 0001-8708

DOI: 10.1016/j.aim.2005.05.003