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Strengthened inequalities for the mean width and the ℓ-norm

Böröczky, K. J.; Fodor, F.; Hug, Daniel

Abstract:
Barthe proved that the regular simplex maximizes the mean width of convex bodies whose John ellipsoid (maximal volume ellipsoid contained in the body) is the Euclidean unit ball; or equivalently, the regular simplex maximizes the ℓ ‐norm of convex bodies whose Löwner ellipsoid (minimal volume ellipsoid containing the body) is the Euclidean unit ball. Schmuckenschläger verified the reverse statement; namely, the regular simplex minimizes the mean width of convex bodies whose Löwner ellipsoid is the Euclidean unit ball. Here we prove stronger stability versions of these results. We also consider related stability results for the mean width and the ℓ ‐norm of the convex hull of the support of centered isotropic measures on the unit sphere.

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Verlagsausgabe §
DOI: 10.5445/IR/1000129550
Veröffentlicht am 10.02.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2021
Sprache Englisch
Identifikator ISSN: 0024-6107, 1469-7750
KITopen-ID: 1000129550
Erschienen in Journal of the London Mathematical Society
Verlag Wiley
Vorab online veröffentlicht am 13.01.2021
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