The curvature entropy inequalities of convex bodies

There are many entropy inequalities in geometry, some of them can be seen as the Minkowski inequalities in the form of entropy, which play important roles in convex geometry. In this article, let and be convex bodies, we introduce the mixed curvature entropy and the curvature entropy with respect to a continuous function . Moreover, we establish the -Minkowski inequalities of the mixed curvature entropy and the curvature entropy for two classes of three-dimensional convex bodies.