2008/07/04 by Marisa Zymonopoulou, Zymonopoulou, Marisa
Mathematics · #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.0807.0779
The complex Busemann-Petty problem asks whether origin symmetric convex bodies in Cn with smaller central hyperplane sections necessarily have smaller volume. The answer is affirmative if n≤ 3 and negative if n≥ 4. In this article we show that the answer remains the same if the volume is replaced by an "almost" arbitrary measure. This result is the complex analogue of Zvavitch's generalization to arbitrary measures of the original real Busemann-Petty problem.