星体的p-极曲率映象与p-仿射表面积

p-Polar Curvature Images of Star Bodies and p-Affine Surface Areas

引进了星体的p-极曲率映象的概念,建立了p-极曲率映象不等式,并给出了一些特殊几何体的p-极曲率映象与其极体的p-仿射表面积乘积的界.作为p-极曲率映象的一个应用,同时研究了p-混合仿射表面积的p-Minkowski型不等式的推广.

This paper introduces the concept of p-polar curvature images of star bodies and establish the p-polar curvature image inequality, and proves the bound for the product of p-affine surface areas of the ppolar curvature images of star bodies and their polar bodies. As an application of p-polar curvature image, we demonstrate the extended p-Minkowski inequality for mixed p-affine surface areas of convex bodies.