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L p John Ellipsoids
Author(s) -
Lutwak Erwin,
Yang Deane,
Zhang Gaoyong
Publication year - 2005
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611504014996
Subject(s) - ellipsoid , mathematics , convex body , regular polygon , ellipsoid method , dual (grammatical number) , legendre polynomials , geometry , pure mathematics , mathematical analysis , convex analysis , convex optimization , geography , geodesy , philosophy , linguistics
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 = ∞, 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. 2000 Mathematics Subject Classification 52A40.