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....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.展开更多
As a generalization of RpK, the mixed radial p-th mean bodies Rp（K,Lμ） have many properties similar to RpK. In this paper, some properties of Rp（K, L,μ） such as monotonicity, transform properties under volume-pr...As a generalization of RpK, the mixed radial p-th mean bodies Rp（K,Lμ） have many properties similar to RpK. In this paper, some properties of Rp（K, L,μ） such as monotonicity, transform properties under volume-preserving linear transformations, etc. were studied. By using the polar coordinate formula for volume and Fubini＇s theorem, V（Rn（K, L,μ）） = V（L） was obtained.展开更多
In this paper, we establish an inequality for the volumes of K and its radial p-th mean body R_pK by L_p-dual mixed volume. Further, the Shephard-type problem and a monotonitic inequality of R_pK are shown when p〉0 .
基金Project supported by the Youth Science Foundation of Shanghai Municipal Commission of Education(Grant No.214511)the Research Grants Council of the HongKong SAR,China(Grant No.HKU7017105P)
文摘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.
基金Project supported by the National Natural Science Foundation of China （Grant Nos.10671117, 30771709）, and the Science and Technology Research Item of Zhejiang Provincial Department of Education （Grant No.20070935）
文摘As a generalization of RpK, the mixed radial p-th mean bodies Rp（K,Lμ） have many properties similar to RpK. In this paper, some properties of Rp（K, L,μ） such as monotonicity, transform properties under volume-preserving linear transformations, etc. were studied. By using the polar coordinate formula for volume and Fubini＇s theorem, V（Rn（K, L,μ）） = V（L） was obtained.
基金Supported by the National Natural Science Foundation of China (10671117)the Science Foundation of China Three Gorges University
文摘In this paper, we establish an inequality for the volumes of K and its radial p-th mean body R_pK by L_p-dual mixed volume. Further, the Shephard-type problem and a monotonitic inequality of R_pK are shown when p〉0 .
