In this paper,the reverse forms of the L p-Busemann-Petty centroid inequality are shown. As the applications of the reverse forms,we obtain the reverse forms of the L p-centroid-affine inequality and an upper bound of...In this paper,the reverse forms of the L p-Busemann-Petty centroid inequality are shown. As the applications of the reverse forms,we obtain the reverse forms of the L p-centroid-affine inequality and an upper bound of the isotropic constant for convex bodies.展开更多
It is shown that a convex body has minimal dual p-surface area among its affine transformations of the same volume if and only if its dual p-surface area measure is isotropic. A double-sided estimate for the （n-1）-d...It is shown that a convex body has minimal dual p-surface area among its affine transformations of the same volume if and only if its dual p-surface area measure is isotropic. A double-sided estimate for the （n-1）-dimensional volume of the intersection of a dual p-surface isotropic convex body in terms of its affine invariant dual p-surface quantity is given. Furthermore, the dual p-isopermetric inequality is obtained.展开更多
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
基金Supported by the National Natural Science Foundation of China (10671117)Academic Mainstay Foundation of Hubei Provincial De-partment of Education (D200729002)Science Foundation of China Three Gorges University
文摘In this paper,the reverse forms of the L p-Busemann-Petty centroid inequality are shown. As the applications of the reverse forms,we obtain the reverse forms of the L p-centroid-affine inequality and an upper bound of the isotropic constant for convex bodies.
基金Project supported by the National Natural Science Foundation of China (Grant No.10671117)
文摘It is shown that a convex body has minimal dual p-surface area among its affine transformations of the same volume if and only if its dual p-surface area measure is isotropic. A double-sided estimate for the （n-1）-dimensional volume of the intersection of a dual p-surface isotropic convex body in terms of its affine invariant dual p-surface quantity is given. Furthermore, the dual p-isopermetric inequality is obtained.
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.
