In this paper, it is proved that the radial pth mean body RpK(p ＞ 0) is homothetic to the difference body DK when K is a simplex. Furthermore, the equality Rp(Rq) = Rq(Rp) is established when p ＞ 0 and q ＞ 0. It is also proved the Brunn-Minkowski inequality of radial pth mean body of simplex and uniqueness property.
convex bodyradial mean bodysimplexcovariogram
倪建华、熊革、CHEUNG Wing-sum
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Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China
Department of Mathematics, HongKong University, HongKong, P. R. China
convex body radial mean body simplex covariogram
上海市青年科学基金Research Grants Council of the HongKong SAR, China
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