数学季刊 ›› 2015, Vol. 30 ›› Issue (4): 596-609.doi: 10.13371/j.cnki.chin.q.j.m.2015.04.013
摘要: For p > 0, Lutwak, Yang and Zhang introduced the concept of Lp-polar projection body Γ-pK of a convex body K in Rn. Let p ≥ 1 and K, L \subset Rnbe two origin-symmetric convex bodies, we consider the question of whether Γ-p K \subset Γ-p L implies \Omegap(L) ≤ \Omegap(K),where \Omegap(K) denotes the Lp-affine surface area of K and K = Voln(K)-1/p K. We prove a necessary and sufficient condition of an analog of the Shephard problem for the Lp-polar projection bodies.
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