Several Properties of the Radial pth Mean Bodies of Convex Bodies
Received:April 19, 2004  
Key Words: the radial $p$th mean body   convex body   radial function.  
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Author NameAffiliation
YUAN Shu-feng Shangyu College, Shaoxing University, Zhejiang 312300, China
Inst. of Appl. Math. Mechanics, Shanghai University, Shanghai 200444, China 
ZHANG Hai-juan Inst. of Appl. Math. Mechanics, Shanghai University, Shanghai 200444, China 
YUAN Jun Dept. of Math., Shanghai University, Shanghai 200444, China 
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Abstract:
      This paper proves that the radial $p$th mean body is invariant under a general linear transformation and that the radial $p$th mean body of an ellipsoid is an ellipsoid. And corresponding to the Blaschke-Santal\'{o} inequality, a reverse inequality for the radial $p$th mean body is given.
Citation:
DOI:10.3770/j.issn:1000-341X.2006.03.029
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