Dual mean Minkowski measures and the Grünbaum conjecture for affine diameters
Dual mean Minkowski measures and the Grünbaum conjecture for affine diameters
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DOI：
10.2140/pjm.2018.292.117
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发表时间：
2018
影响因子：
0.6
通讯作者：
Qi Guo;G. Tóth
中科院分区：
文献类型：
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作者：
Qi Guo;G. Tóth
欧几里得矢量空间中凸体C X维n(≥2),我们定义两个sub-arithmetic单调序列{σC k} k≥1和{σo C k} k≥1的内部函数C k成员”是指在维闵可夫斯基措施k”的点态双:σo C k (o) =σ有限公司k (o), C o∈int,和公司的双重(极性)C与o .的措施(反)对称C以下感觉:1≤σC k (o),σC k (o)≤2 k + 1。本工作由第二作者于2015年1月在中国苏州停留，由中国国家科学基金（NSF）资助（11271282）。
For a convex body C in a Euclidean vector space X of dimension n (≥ 2), we define two sub-arithmetic monotonic sequences {σC,k}k≥1 and {σo C,k}k≥1 of functions on the interior of C. The k-th members are “mean Minkowski measures in dimension k” which are pointwise dual: σo C,k(O) = σCO,k(O), where O ∈ int C, and CO is the dual (polar) of C with respect to O. They are measures of (anti-)symmetry of C in the following sense: 1 ≤ σC,k(O), σ C,k(O) ≤ k + 1 2 . This work including the stay of the second author in Suzhou, China, in January 2015, was supported by the NSF China, No. 11271282.