The complex Busemann-Petty problem on sections of convex bodies

2007/07/26 by Koldobsky, A., König, H., Zymonopoulou, M.
#52A20 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.0707.3851

Abstract

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

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