Hao Jing, Jog Varun
Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, USA.
Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA.
Entropy (Basel). 2019 Aug 18;21(8):809. doi: 10.3390/e21080809.
We establish lower bounds on the volume and the surface area of a geometric body using the size of its slices along different directions. In the first part of the paper, we derive volume bounds for convex bodies using generalized subadditivity properties of entropy combined with entropy bounds for log-concave random variables. In the second part, we investigate a new notion of Fisher information which we call the L 1 -Fisher information and show that certain superadditivity properties of the L 1 -Fisher information lead to lower bounds for the surface areas of polyconvex sets in terms of its slices.
我们利用几何物体沿不同方向的切片尺寸来确定其体积和表面积的下界。在本文的第一部分，我们结合对数凹随机变量的熵界，利用熵的广义次可加性性质推导凸体的体积界。在第二部分，我们研究一种新的 Fisher 信息概念，我们称之为 L1 - Fisher 信息，并表明 L1 - Fisher 信息的某些超可加性性质导致多凸集表面积关于其切片的下界。
