Journal of Shanghai University(Natural Science Edition)

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The lp-Norm of Convex Bodies

WANG Zhi-wen,YUAN Jun,LENG Gang-song   

  1. School of Sciences, Shanghai University, Shanghai 200444, China
  • Received:2006-07-05 Revised:1900-01-01 Online:2007-06-30 Published:2007-06-30
  • Contact: LENG Gang-song

Abstract: The article extends the l norm of the convex body to the Lp space. We introduce the lp norm and proof that if convex body's Lowner ellipsoid (the minimal volume ellipsoid containing the convex) is the Euclidean unit ball, and the octahedron has the maximal lp norm. We also give the BlaschkeSanatlaó type inequality of lp norm.

Key words: circumradius, inequality, inradius, lp norm, convex body

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