In this paper, the concepts of the ith L;-mixed affine surface area and Lp-polar curvature images are introduced, some new inequalities connecting these new notions with Lρ-centroid bodies and ρ-Blaschke bodies are ...In this paper, the concepts of the ith L;-mixed affine surface area and Lp-polar curvature images are introduced, some new inequalities connecting these new notions with Lρ-centroid bodies and ρ-Blaschke bodies are showed. Moreover, a Blaschke-Santalo type inequality for Lρ-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
Lutwak showed the Busemann-Petty type problem(also called the Shephard type problem)for the centroid bodies.Grinberg and Zhang gave an affirmation and a negative form of the Busemann-Petty type problem for the L_(p)-c...Lutwak showed the Busemann-Petty type problem(also called the Shephard type problem)for the centroid bodies.Grinberg and Zhang gave an affirmation and a negative form of the Busemann-Petty type problem for the L_(p)-centroid bodies.In this paper,we obtain an affirmation form and two negative forms of the BusemannPetty type problem for the general L_(p)-centroid bodies.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;-mixed affine surface area and Lp-polar curvature images are introduced, some new inequalities connecting these new notions with Lρ-centroid bodies and ρ-Blaschke bodies are showed. Moreover, a Blaschke-Santalo type inequality for Lρ-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 in part by the Natural Science Foundation of China (Grant No.11371224)。
文摘Lutwak showed the Busemann-Petty type problem(also called the Shephard type problem)for the centroid bodies.Grinberg and Zhang gave an affirmation and a negative form of the Busemann-Petty type problem for the L_(p)-centroid bodies.In this paper,we obtain an affirmation form and two negative forms of the BusemannPetty type problem for the general L_(p)-centroid bodies.
