Abstract
We prove an extension of the classical John's Theorem, that characterises the ellipsoid of maximal volume position inside a convex body by the existence of some kind of decomposition of the identity, obtaining some results for maximal volume position of a compact and connected set inside a convex set with nonempty interior. By using those results we give some estimates for the outer volume ratio of bodies not necessarily convex.
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Bastero, J., Romance, M. John's Decomposition of the Identity in the Non-Convex Case. Positivity 6, 1–16 (2002). https://doi.org/10.1023/A:1012087231191
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DOI: https://doi.org/10.1023/A:1012087231191