The complex Busemann-Petty problem for arbitrary measures |
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Authors: | Marisa Zymonopoulou |
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Institution: | (1) Department of Mathematics, Case Western University, Cleveland, OH 44106, USA |
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Abstract: | The complex Busemann-Petty problem asks whether origin symmetric convex bodies in with smaller central hyperplane sections necessarily have smaller volume. The answer is affirmative if and negative if . 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.
Received: 6 May 2008 |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 52A20 |
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