Staff Publications

Staff Publications

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    'Staff publications' is the digital repository of Wageningen University & Research

    'Staff publications' contains references to publications authored by Wageningen University staff from 1976 onward.

    Publications authored by the staff of the Research Institutes are available from 1995 onwards.

    Full text documents are added when available. The database is updated daily and currently holds about 240,000 items, of which 72,000 in open access.

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Record number 553325
Title Isotropic measures and maximizing ellipsoids : Between John and Loewner
Author(s) Artstein-Avidan, Shiri; Katzin, David
Source Proceedings of the American Mathematical Society 146 (2018)12. - ISSN 0002-9939 - p. 5379 - 5390.
DOI https://doi.org/10.1090/proc/14180
Department(s) Farm Technology
Publication type Refereed Article in a scientific journal
Publication year 2018
Keyword(s) Convex bodies - Ellipsoids - Isotropic position - John position - Loewner position - M position
Abstract

We define a one-parametric family of positions of a centrally symmetric convex body K which interpolates between the John position and the Loewner position: for r>0, we say that K is in maximal intersection position of radius r if Vol n (K ∩ rB n 2 ) ≥ Vol n (K ∩ rTB n 2 ) for all T ∈ SL n . We show that under mild conditions on K, each such position induces a corresponding isotropic measure on the sphere, which is simply the normalized Lebesgue measure on r −1 K ∩ S n−1 . Inparticular, for r M satisfying r n M κ n =Vol n (K), the maximal intersection position of radius r M is an M-position, so we get an M-position with an associated isotropic measure. Lastly, we give an interpretation of John’s theorem on contact points as a limit case of the measures induced from the maximal intersection positions.

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