The Busemann-Petty problem for arbitrary measures
نویسندگان
چکیده
منابع مشابه
May 21, 2014 AN ISOMORPHIC VERSION OF THE BUSEMANN-PETTY PROBLEM FOR ARBITRARY MEASURES
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 isomo...
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Abstract. The aim of this paper is to study properties of sections of convex bodies with respect to different types of measures. We present a formula connecting the Minkowski functional of a convex symmetric body K with the measure of its sections. We apply this formula to study properties of general measures most of which were known before only in the case of the standard Lebesgue measure. We ...
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This question is known as the generalized Busemann-Petty problem. For i = n − 1, the problem was posed by Busemann and Petty [2] in 1956. It has a long history, and the answer is affirmative if and only if n ≤ 4; see [3], [8], [11]. For the generalized Busemann-Petty problem the following statements are known. If i = 2, n = 4, an affirmative answer follows from that in the case i = n − 1. If 3 ...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2005
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-004-0611-5