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- W2952052356 abstract "The classical Brunn-Minkowski inequality states that for $A_1,A_2subsetR^n$ compact, $$ |A_1+A_2|^{1/n}ge |A_1|^{1/n}+|A_2|^{1/n}eqno(1) $$ where $|cdot|$ denotes the Lebesgue measure on $R^n$. In 1986 V. Milman {bf [Mil 1]} discovered that if $B_1$ and $B_2$ are balls there is always a relative position of $B_1$ and $B_2$ for which a perturbed inverse of $(1)$ holds. More precisely:lqlq{sl There exists a constant $C>0$ such that for all $ninN$ and any balls $B_1,B_2subsetR^n$ we can find a linear transformation $ucolonR^ntoR^n$ with $|{rm det}(u)|=1$ and $$|u(B_1)+B_2|^{1/n}le C(|B_1|^{1/n}+|B_2|^{1/n})$$} The aim of this paper is to extend this Milman's result to a larger class of sets." @default.
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- W2952052356 date "1995-01-03" @default.
- W2952052356 modified "2023-09-26" @default.
- W2952052356 title "An extension of Milman's reverse Brunn-Minkowski inequality" @default.
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- W2952052356 doi "https://doi.org/10.48550/arxiv.math/9501210" @default.
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