论文标题
Pinsker的不平等和相关的Monge-ampère方程，用于日志凹功能
Pinsker inequalities and related Monge-Ampère equations for log concave functions
论文作者
论文摘要
在本文中，我们进一步开发了对数孔函数及其相关不平等的F-Diverencence的理论。我们建立了Pinsker的不平等和新的仿射不变的熵不平等。在功能性仿射表面积方面，我们获得了功能性仿射表面积和下限和上限的新不平等。功能性不平等导致凸体L_P-affine表面积的新不平等。
In this paper we further develop the theory of f-divergences for log-concave functions and their related inequalities. We establish Pinsker inequalities and new affine invariant entropy inequalities. We obtain new inequalities on functional affine surface area and lower and upper bounds for the Kullback-Leibler divergence in terms of functional affine surface area. The functional inequalities lead to new inequalities for L_p-affine surface areas for convex bodies.
