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Centres of Convex Sets inLpMetrics

✍ Scribed by Krzysztof Przesławski

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 397 KB
Volume: 85
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1996.0043

No coin nor oath required. For personal study only.

✦ Synopsis

It is shown that for each convex body A/R n there exists a naturally defined family G A /C(S n&1 ) such that for every g # G A , and every convex function f : R Ä R the mapping y [ S n&1 f ( g(x)&( y, x)) d_(x) has a minimizer which belongs to A. As an application, approximation of convex bodies by balls with respect to L p metrics is discussed.

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