Let K be a 1-unconditional convex bodies in Euclidean spaces.We study the asymptotic properties of two affine invariants m2（K） and S2（K） for a random simplex inside K.As an application,we discuss the asymptotic pr...Let K be a 1-unconditional convex bodies in Euclidean spaces.We study the asymptotic properties of two affine invariants m2（K） and S2（K） for a random simplex inside K.As an application,we discuss the asymptotic properties of two affine invariants m2（Bpn ） and S2（Bpn ）,where Bpn = {x ∈ Rn ： ‖x‖ p 1}.展开更多
In this paper,we study the smoothness of the Steiner symmetrization process and generalize the Steiner symmetrization of functions in Sobolev space to the Steiner symmetrization of convex body.We prove that for a C^(1...In this paper,we study the smoothness of the Steiner symmetrization process and generalize the Steiner symmetrization of functions in Sobolev space to the Steiner symmetrization of convex body.We prove that for a C^(1)convex body,its Steiner symmetral is still a C^(1)convex body.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.10671119)
文摘Let K be a 1-unconditional convex bodies in Euclidean spaces.We study the asymptotic properties of two affine invariants m2（K） and S2（K） for a random simplex inside K.As an application,we discuss the asymptotic properties of two affine invariants m2（Bpn ） and S2（Bpn ）,where Bpn = {x ∈ Rn ： ‖x‖ p 1}.
基金Supported by the National Natural Science Foundation of China(11971080)Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN202000838)+1 种基金the Basic and Advanced Research Project of Chongqing(cstc2018jcyjAX0790,cstc2020jcyj-msxmX0328)the Innovative Project of Chongqing Technology and Business University(yjscxx2021-112-56)
文摘In this paper,we study the smoothness of the Steiner symmetrization process and generalize the Steiner symmetrization of functions in Sobolev space to the Steiner symmetrization of convex body.We prove that for a C^(1)convex body,its Steiner symmetral is still a C^(1)convex body.
