Abstract: 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 p-polar 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.

Key words: inequalities, p-affine surface area, p-polar curvature image, star body