The Busemann–Petty problem in hyperbolic and spherical spaces

Abstract

The Busemann–Petty problem asks whether origin-symmetric convex bodies in R n 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.