Dual mixed volumes and the slicing problem
Dual mixed volumes and the slicing problem
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DOI：
10.1016/j.aim.2005.09.008
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发表时间：
2005-12
影响因子：
1.7
通讯作者：
E. Milman
中科院分区：
文献类型：
--
作者：
E. Milman
我们开发了一种使用双混合体积的技术来研究某些类别空间的各向同性常数。特别是，我们恢复、加强和推广了 Ball 和 Junge 关于子空间的各向同性常数和 Lpand 相关空间的商的结果。使用广义交集体，还可以将这些结果扩展到 p 的负值。特别是，我们证明了包含在相交体中的凸体的各向同性常数受后者的平均半径与前者的体积半径之比的限制（直到一个常数）。我们还展示了如何使用 type 或 cotype 2 轻松证明任何各向同性测度的不等式。
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 Lpand 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.