Abstract
The Busemann–Petty problem asks whether symmetric convex bodies in R n with smaller central hyperplane sections necessarily have smaller n-dimensional volume. The solution has recently been completed, and the answer is affirmative if n⩽4 and negative if n⩾5. In this article we present a short proof of the affirmative result and its generalization using the Funk–Hecke formula for spherical harmonics.
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