Polar duals of convex bodies
Polar duals of convex bodies
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DOI：
10.1090/s0002-9939-1991-1057954-7
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发表时间：
1991-03
期刊：
影响因子：
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通讯作者：
M. Ghandehari
中科院分区：
文献类型：
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作者：
M. Ghandehari
给出了 Firey 的以下结果的推广和对偶版本：平面凸体及其极对偶的混合面积至少为 π。我们为任何指数的对偶横截面测度与其极对偶测度的乘积给出了一个尖锐的上限。凸体 K 和凸增实值函数的一般结果给出了恒定宽度的集合和具有等弦点的集合作为特殊情况的不等式
A generalizationand the dual version of the following result due to Firey is given: the mixed area of a plane convex body and its polar dual is at least π. We give a sharp upper bound for the product of the dual cross-sectional measure of any index and that of its polar dual. A general result for a convex body K and a convex increasing real-valued function gives inequalities for sets of constant width and sets with equichordal points as special cases