论文标题
凸体上的曲率功能
Curvature functionals on convex bodies
论文作者
论文摘要
我们研究了出现在最近建立的$ l_p $ steiner公式中的加权$ l_p $ affine表面积。我们证明它们是凸面上的估值，并证明了它们的等量不平等。我们表明，它们与凸形机构的圆锥体测量及其极性的$ f $差异有关，即Kullback-Leibler Divergence和Rényi-Divergence。
We investigate the weighted $L_p$ affine surface areas which appear in the recently established $L_p$ Steiner formula of the $L_p$ Brunn Minkowski theory. We show that they are valuations on the set of convex bodies and prove isoperimetric inequalities for them. We show that they are related to $f$ divergences of the cone measures of the convex body and its polar, namely the Kullback-Leibler divergence and the Rényi-divergence.
