The complex Busemann-Petty problem on sections of convex bodies

Abstract

The complex Busemann-Petty problem asks whether origin symmetric convex bodies in $\C^n$ with smaller central hyperplane sections necessarily have smaller volume. We prove that the answer is affirmative if $n\le 3$ and negative if $n\ge 4.$

arXiv comment18 pages

References in corpus (1)

• Positive definite distributions and subspaces of $L_{-p}$ with applications to stable processes