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inertial ellipsoid

Proceedings of the London Mathematical Society (1)

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$L_p$ John Ellipsoids
Erwin Lutwak, Deane Yang, Gaoyong Zhang
Journal:

Proceedings of the London Mathematical Society / Volume 90 / Issue 2 / March 2005

Published online by Cambridge University Press:

25 February 2005, pp. 497-520

Print publication:

March 2005
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It is shown that the classical John ellipsoid, the Petty ellipsoid and a recently discovered ‘dual’ of the Legendre ellipsoid are all special cases ($p = \infty$, $p = 1$ and $p = 2$) of a family of $L_p$ ellipsoids which can be associated with a fixed convex body. This insight allows for a unified view of, alternative approaches to, and extensions of some basic results in convex geometry.