论文标题
关于Busemann交叉路口不平等的概括
On a generalization of Busemann's intersection inequality
论文作者
论文摘要
Busemann的交叉路口不等式在体内的体积本身的体积方面为星体交叉体的体积提供了上限。 Koldobsky，Paouris和Zymonopoulou询问了$ K $ -Intternection Bodies是否有类似的结果。我们解决了在Banach-Mazur距离靠近欧几里得球的星体的问题。在$ k $与尺寸成正比的情况下，我们还改善了由Koldobsky，Paouris和Zymonopoulou获得的界限。
Busemann's intersection inequality gives an upper bound for the volume of the intersection body of a star body in terms of the volume of the body itself. Koldobsky, Paouris, and Zymonopoulou asked if there is a similar result for $k$-intersection bodies. We solve this problem for star bodies that are close to the Euclidean ball in the Banach-Mazur distance. We also improve a bound obtained by Koldobsky, Paouris, and Zymonopoulou for general star bodies in the case when $k$ is proportional to the dimension.
