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- W2952368903 abstract "A translation body of a convex body is the convex hull of two of its translates intersecting each other. In the 1950s, Rogers and Shephard found the extremal values, over the family of $n$-dimensional convex bodies, of the maximal volume of the translation bodies of a given convex body. In our paper, we introduce a normed version of this problem, and for the planar case, determine the corresponding quantities, with one exception, for the four types of volumes regularly used in the literature: Busemann, Holmes-Thompson, and Gromov's mass and mass*. We examine the problem also for higher dimensions, and for centrally symmetric convex bodies." @default.
- W2952368903 created "2019-06-27" @default.
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- W2952368903 date "2013-08-12" @default.
- W2952368903 modified "2023-09-27" @default.
- W2952368903 title "On a normed version of a Rogers-Shephard type problem" @default.
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