论文标题
异肥性不平等
Isobarycentric Inequalities
论文作者
论文摘要
我们证明了以下等等类型的不等式：给定有限的borel borel量度，$ {\ mathbb r}^n $，在所有带有开处方的Barycenter的子集中，半个空格都具有最大程度的措施。结果，我们朝着解决Henk和Pollehn问题的解决方案方面取得了进展，这相当于平行曲线和中心凸体的对数 - 米科夫斯基的不平等。我们对问题的概率方法也引起了有关某些对数符号随机变量的截断平均值的几种不平等和猜想。
We prove the following isoperimetric type inequality: Given a finite absolutely continuous Borel measure on ${\mathbb R}^n$, halfspaces have maximal measure among all subsets with prescribed barycenter. As a consequence, we make progress towards a solution to a problem of Henk and Pollehn, which is equivalent to a Log-Minkowski inequality for a parallelotope and a centered convex body. Our probabilistic approach to the problem also gives rise to several inequalities and conjectures concerning the truncated mean of certain log-concave random variables.
