$L_p$ John Ellipsoids

• Autores: Erwin Lutwak, Deane Yang, Gaoyong Zhang
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 90, Nº 2, 2005, págs. 497-520
• Idioma: inglés
• DOI: 10.1112/s0024611504014996
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• Resumen

  • 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.