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Proceedings of the Edinburgh Mathematical Society (1)

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DUAL $L_{p}$ JOHN ELLIPSOIDS
Wuyang Yu, Gangsong Leng, Donghua Wu
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 50 / Issue 3 / October 2007

Published online by Cambridge University Press:

08 January 2008, pp. 737-753
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In this paper, the dual $L_p$ John ellipsoids, which include the classical Löwner ellipsoid and the Legendre ellipsoid, are studied. The dual $L_p$ versions of John's inclusion and Ball's volume-ratio inequality are shown. This insight allows for a unified view of some basic results in convex geometry and reveals further the amazing duality between Brunn–Minkowski theory and dual Brunn–Minkowski theory.