The Busemann-Petty problem via spherical harmonics |
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Authors: | Alexander Koldobsky |
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Institution: | Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, USA |
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Abstract: | The Busemann-Petty problem asks whether symmetric convex bodies in 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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Keywords: | 52A20 |
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