An isomorphic version of the Busemann–Petty problem for arbitrary measures

  title={An isomorphic version of the Busemann–Petty problem for arbitrary measures},
  author={Alexander Koldobsky and Artem Zvavitch},
The Busemann-Petty problem for an arbitrary measure μ with non-negative even continuous density in R asks whether origin-symmetric convex bodies in R with smaller (n − 1)-dimensional measure μ of all central hyperplane sections necessarily have smaller measure μ. It was shown in [Zv] that the answer to this problem is affirmative for n ≤ 4 and negative for n ≥ 5. In this paper we prove an isomorphic version of this result. Namely, if K,M are origin-symmetric convex bodies in R such that μ(K… CONTINUE READING


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