On the Busemann-Petty Problem Concerning Central Sections of Centrally Symmetric Convex-Bodies
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چکیده
We present a method which shows that in E3 the Busemann-Petty problem, concerning central sections of centrally symmetric convex bodies, has a positive answer. Together with other results, this settles the problem in each dimension. In [BP], Busemann and Petty asked the following question, which resulted from reformulating a problem in Minkowskian geometry. Suppose K\ and K2 are convex bodies in «-dimensional Euclidean space E" which are centered (centrally symmetric with center at the origin) and such that A„_1(A-1nw±)<A„_,(A'2nwx), for all u in the unit sphere Sn~l . Then is it true that
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تاریخ انتشار 1994