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, combining with the L_p-dual geominimal surface area and the general L_p-centroid bodies, we research the Shephard type problems for general L_p-centroid 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.
文摘In this paper, combining with the L_p-dual geominimal surface area and the general L_p-centroid bodies, we research the Shephard type problems for general L_p-centroid bodies.