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- W3027836626 abstract "The isodiametric inequality states that the Euclidean ball maximizes the volume among all convex bodies of a given diameter. We are motivated by a conjecture of Makai Jr. on the reverse question: Every convex body has a linear image whose isodiametric quotient is at least as large as that of a regular simplex. We relate this reverse isodiametric problem to minimal volume enclosing ellipsoids and to the Dvoretzky–Rogers-type problem of finding large volume simplices in any decomposition of the identity matrix. As a result, we solve the reverse isodiametric problem for o-symmetric convex bodies and obtain a strong asymptotic bound in the general case. Using the Cauchy–Binet formula for minors of a product of matrices, we obtain Dvoretzky–Rogers-type volume bounds which are of independent interest." @default.
- W3027836626 created "2020-05-29" @default.
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- W3027836626 date "2020-05-22" @default.
- W3027836626 modified "2023-10-17" @default.
- W3027836626 title "On the reverse isodiametric problem and Dvoretzky–Rogers-type volume bounds" @default.
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- W3027836626 doi "https://doi.org/10.1007/s13398-020-00867-7" @default.
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