The Busemann-Petty problem for arbitrary measures

By Artem Zvavitch. 2004

68 citations recorded by the source corpus.

Abstract.The Busemann-Petty problem asks whether symmetric convex bodies in ℝn with smaller (n−1)-dimensional volume of central hyperplane sections necessarily have smaller n-dimensional volume. The answer to this problem is affirmative for n≤4 and negative for n≥5. In this paper we generalize the Busemann-Petty problem to essentially arbitrary measure in place of the volume. We also present applications of the latter result by proving several inequalities concerning the measure of sections of convex symmetric bodies in ℝn.

Subfields: Applied Mathematics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/11b0843e90bd7106b7767fd7495177ef6eac857d

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In Applied Mathematics

1. Emanuel Milman
2. A. V. Kolesnikov
3. Zoltán M. Balogh
4. Alexandru Krist'aly
5. Fabio Cavalletti
6. W. Wylie
7. Joaquim Martín
8. Mario Milman

In Molecular Biology

1. Emanuel Milman

Citations in the corpus

• Generalized intersection bodies (2005, methodology): “r is positive if L is a Euclidean ball and K is convex and sufficiently close to L. Several other generalizations of GENERALIZED INTERSECTION BODIES 3 the Busemann-Petty problem were treated in [RZ04], [Zva05], [Yas05], [Yas06]. Before defining the class of k-Busemann-Petty bodies we shall need to intr”