In this paper,the concepts of the ith L_p-mixed affine surface area and L_p-polar curvature images are introduced,some new inequalities connecting these new notions with L_p-centroid bodies and p-Blaschke bodies are s...In this paper,the concepts of the ith L_p-mixed affine surface area and L_p-polar curvature images are introduced,some new inequalities connecting these new notions with L_p-centroid bodies and p-Blaschke bodies are showed.Moreover,a Blaschke-Santaio type inequality for L_p-mixed affine surface area is established.Our results also imply the similar to the inequalities for Marcus-Lopes,Bergstrom and Ky Fan.展开更多
Let X be a compact set which is laminated by parabolic Riemiann surfaces. For the CR positive line bundle L, there exists an integer N ∈ N such that for any s 〉 N and any continuous v ∈∧^（0,1）X×L^×s, t...Let X be a compact set which is laminated by parabolic Riemiann surfaces. For the CR positive line bundle L, there exists an integer N ∈ N such that for any s 〉 N and any continuous v ∈∧^（0,1）X×L^×s, there exists a continuous u ∈ L^×s solving δb^-u = v.展开更多
According to the notion of Orlicz mixed volume, in this paper, we extend L;-dual affine surface area to the Orlicz version. Further, we obtain the affine isoperimetric inequality and the Blachke-Santaló inequalit...According to the notion of Orlicz mixed volume, in this paper, we extend L;-dual affine surface area to the Orlicz version. Further, we obtain the affine isoperimetric inequality and the Blachke-Santaló inequality for the dual Orlicz affine surface area. Besides, we also get the monotonicity inequality for Orlicz dual affine surface area.展开更多
Abstract In this article, we put forward the concept of the （i,j）-type Lp-mixed alpine surface area, such that the notion of Lp-affine surface area which be shown by Lutwak is its special cases. Furthermore, applyin...Abstract In this article, we put forward the concept of the （i,j）-type Lp-mixed alpine surface area, such that the notion of Lp-affine surface area which be shown by Lutwak is its special cases. Furthermore, applying this concept, the Minkowski inequality for the （i, -p）-type Lp-mixed affine surface area and the extensions of the well-known Lp-Petty atone projection inequality are established, respectively. Besides, we give an affirmative answer for the generalized Lp-Winterniz monotonicity problem.展开更多
基金Supported by the NNSF of China(11161024)Supported by the NSF of Jiangxi Province (2010GZC0115)
文摘In this paper,the concepts of the ith L_p-mixed affine surface area and L_p-polar curvature images are introduced,some new inequalities connecting these new notions with L_p-centroid bodies and p-Blaschke bodies are showed.Moreover,a Blaschke-Santaio type inequality for L_p-mixed affine surface area is established.Our results also imply the similar to the inequalities for Marcus-Lopes,Bergstrom and Ky Fan.
基金Supported by the National Natural Science Foundation of China(11271359)
文摘Let X be a compact set which is laminated by parabolic Riemiann surfaces. For the CR positive line bundle L, there exists an integer N ∈ N such that for any s 〉 N and any continuous v ∈∧^（0,1）X×L^×s, there exists a continuous u ∈ L^×s solving δb^-u = v.
基金Supported by the National Natural Science Foundation of China(11161019,11561020)the Science and Technology Plan of Gansu Province(145RJZG227)
文摘According to the notion of Orlicz mixed volume, in this paper, we extend L;-dual affine surface area to the Orlicz version. Further, we obtain the affine isoperimetric inequality and the Blachke-Santaló inequality for the dual Orlicz affine surface area. Besides, we also get the monotonicity inequality for Orlicz dual affine surface area.
基金Supported by National Natural Science Foundation of China(Grant Nos.11161019 and 11371224)the Science and Technology Plan of the Gansu Province(Grant No.145RJZG227)
文摘Abstract In this article, we put forward the concept of the （i,j）-type Lp-mixed alpine surface area, such that the notion of Lp-affine surface area which be shown by Lutwak is its special cases. Furthermore, applying this concept, the Minkowski inequality for the （i, -p）-type Lp-mixed affine surface area and the extensions of the well-known Lp-Petty atone projection inequality are established, respectively. Besides, we give an affirmative answer for the generalized Lp-Winterniz monotonicity problem.
