对偶混合矩阵与切片问题
Dual Mixed Volumes and the Slicing Problem
摘要：
本文发展了一种利用对偶混合体积的方法来研究某些空间类的迷向常数。特别地，我们恢复、加强和推广了Ball和Junge关于L_p及相关空间的子空间和子空间的迷向常数的结果.推广这些结果的负值p也得到，使用广义相交机构。特别地，我们证明了包含在相交体中的凸体的各向同性常数由相交体的平均半径与前者的体积半径之比所限定（直到常数）。我们还展示了如何类型或cotype 2可以用来很容易地证明任何各向同性措施的不平等。
英文摘要：
We develop a technique using dual mixed-volumes to study the isotropic constants of some classes of spaces. In particular, we recover, strengthen and generalize results of Ball and Junge concerning the isotropic constants of subspaces and quotients of L_p and related spaces. An extension of these results to negative values of p is also obtained, using generalized intersection-bodies. In particular, we show that the isotropic constant of a convex body which is contained in an intersection-body is bounded (up to a constant) by the ratio between the latter's mean-radius and the former's volume-radius. We also show how type or cotype 2 may be used to easily prove inequalities on any isotropic measure.
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