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- W4367694311 abstract "Given a convex body $K,$ the difference body of $K,$ denoted $DK,$ and the polar projection body of $K,$ denoted $Pi^circ K$ are symmetric convex bodies which admit two affine-invariant inequalities: the inequalities of Rogers-Shephard and Zhang, written succinctly as $text{vol}_n(DK)leq binom{2n}{n} text{vol}_n(K) leq text{vol}_n(ntext{vol}_n(K)Pi^circ K).$ There is equality throughout if, and only if, $K$ is a $n$-dimensional simplex. Continuing on the work of Schneider, who defined a higher order analogue of the difference body and proved the associated Rogers-Shephard inequality, we extended this concept to the projection operator in the prequel to this work and proved the associated Zhang-type inequality. Now, we show these ideas are compatible with measures that have density." @default.
- W4367694311 created "2023-05-03" @default.
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- W4367694311 date "2023-04-30" @default.
- W4367694311 modified "2023-09-24" @default.
- W4367694311 title "On Higher-Order Extensions of the Weighted Projection Body Operator" @default.
- W4367694311 doi "https://doi.org/10.48550/arxiv.2305.00479" @default.
- W4367694311 hasPublicationYear "2023" @default.
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