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- W4214892894 abstract "For p>−1 and α-homogeneous measure μ on Rn with α≠−p, this paper considers the measure-comparison problem for the polar (p,μ)-centroid operator Γp,μ⁎. Namely, if K,L are origin-symmetric convex bodies in Rn with satisfyingΓp,μ⁎K⊂Γp,μ⁎L, does it follow thatpα+pμ(L)p≤pα+pμ(K)p? This paper shows that the answer is confirmative when −1<p<0,α+p<0, and negative when p≥0, or −1<p<0,α+p>0. In the negative cases, we also give a solution to the isomorphic version of the above problem. Namely, the condition Γp,μ⁎K⊂Γp,μ⁎L implies thatμ(L)1/α≤nμ(K)1/α." @default.
- W4214892894 created "2022-03-05" @default.
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- W4214892894 date "2022-06-01" @default.
- W4214892894 modified "2023-10-17" @default.
- W4214892894 title "The measure-comparison problem for polar (p,μ)-centroid bodies" @default.
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- W4214892894 doi "https://doi.org/10.1016/j.aam.2022.102332" @default.
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