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- W4310561522 abstract "We consider the problem of finding the best function $varphi_n:[0,1]tomathbb{R}$ such that for any pair of convex bodies $K,Linmathbb{R}^n$ the following Brunn-Minkowski type inequality holds $$ |K+_theta L|^frac{1}{n}geqvarphi_n(theta)(|K|^frac{1}{n}+|L|^frac{1}{n}), $$ where $K+_theta L$ is the $theta$-convolution body of $K$ and $L$. We prove a sharp inclusion of the family of Ball's bodies of an $alpha$-concave function in its super-level sets in order to provide the best possible function in the range $left(frac{3}{4}right)^nleqthetaleq1$, characterizing the equality cases." @default.
- W4310561522 created "2022-12-12" @default.
- W4310561522 creator A5034866938 @default.
- W4310561522 creator A5054921082 @default.
- W4310561522 date "2022-11-30" @default.
- W4310561522 modified "2023-09-26" @default.
- W4310561522 title "Brunn-Minkowski inequality for $theta$-convolution bodies via Ball's bodies" @default.
- W4310561522 doi "https://doi.org/10.48550/arxiv.2211.17069" @default.
- W4310561522 hasPublicationYear "2022" @default.
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