On the Analog of Shephard Problem for Lp-p olar Pro jection Bo dies

摘要

For p>0, Lutwak, Yang and Zhang introduced the concept of Lp-polar projection bodyΓ−pK of a convex body K in Rn. Let p≥1 and K, L⊂Rn be two origin-symmetric convex bodies, we consider the question of whetherΓ−p eK ⊂Γ−p eL impliesΩp(L)≤Ωp(K), where Ωp(K) denotes the Lp-affine surface area of K and eK = Voln(K)−1p K. We prove a necessary and sufficient condition of an analog of the Shephard problem for the Lp-polar projection bodies.