Dual Mean Minkowski Measures and the Grünbaum Conjecture for Affine Diameters
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چکیده
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.
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تاریخ انتشار 2015