An analytic solution to the Busemann-Petty problem on sections of convex bodies

@article{Gardner1999AnAS,
  title={An analytic solution to the Busemann-Petty problem on sections of convex bodies},
  author={Richard J. Gardner and Alexander Koldobsky and Thomas Schlumprecht},
  journal={Annals of Mathematics},
  year={1999},
  volume={149},
  pages={691-703}
}
  • Richard J. Gardner, Alexander Koldobsky, Thomas Schlumprecht
  • Published 1999
  • Mathematics
  • Annals of Mathematics
  • We derive a formula connecting the derivatives of parallel section functions of an origin-symmetric star body in R n with the Fourier transform of powers of the radial function of the body. A parallel section function (or (ni 1)dimensional X-ray) gives the ((ni 1)-dimensional) volumes of all hyperplane sections of the body orthogonal to a given direction. This formula provides a new characterization of intersection bodies in R n and leads to a unifled analytic solution to the Busemann-Petty… CONTINUE READING

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