The curvature entropy inequalities of convex bodies - Zhang Deyan (Open Mathematics)
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 PP and QQ be convex bodies, we introduce the mixed curvature entropy Mf(P,Q)M_{f}\left(P,Q) and the curvature entropy Ef(P,Q)E_{f}\left(P,Q) with respect to a continuous function ff. Moreover, we establish the log\log -Minkowski inequalities of the mixed curvature entropy and the curvature entropy for two classes of three-dimensional convex bodies.