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An application of the fourier transform to sections of star bodies

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Abstract

We express the volume of central hyperplane sections of star bodies inR n in terms of the Fourier transform of a power of the radial function, and apply this result to confirm the conjecture of Meyer and Pajor on the minimal volume of central sections of the unit balls of the spaces n p with 0<p<2.

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Correspondence to Alexander Koldobsky.

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Research supported in part by the NSF Grant DMS-9531594.

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Koldobsky, A. An application of the fourier transform to sections of star bodies. Isr. J. Math. 106, 157–164 (1998). https://doi.org/10.1007/BF02773465

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  • DOI: https://doi.org/10.1007/BF02773465

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