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• W1492649312 abstract "We give a description of an affine mapping T involving contact pairs of two general convex bodies K and L, when T(K) is in a position of maximal volume in L. This extends the classical John's theorem of 1948, and is applied to the solution of a problem of Grünbaum; namely, any two convex bodies K and L in ℝ n have non-degenerate affine images K′ and L′ such that K′ ⊂ L′ ⊂ - n K′. As a corollary, we obtain that if L has a center of symmetry, then there are non-degenerate affine images K″ and L″ of K and L such that K″ ⊂ L″ ⊂ n K″. Other applications to volume ratios and distance estimates are given. In particular, the Banach-Mazur distance between the n-dimensional simplex and any centrally symmetric convex body is equal to n." @default.
• W1492649312 created "2016-06-24" @default.
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• W1492649312 date "2004-09-01" @default.
• W1492649312 modified "2023-10-02" @default.
• W1492649312 title "John's Decomposition in the General Case and Applications" @default.
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• W1492649312 doi "https://doi.org/10.4310/jdg/1102536711" @default.
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