A remark on the slicing problem

作者：Giannopoulos Apostolos^*; Paouris Grigoris; Vritsiou Beatrice Helen

来源：Journal of Functional Analysis, 2012, 262(3): 1062-1086.

DOI：10.1016/j.jfa.2011.10.011

• Convex body
• Isotropic body
• Isotropic constant
• Centroid bodies

The purpose of this article is to describe a reduction of the slicing problem to the study of the parameter I-1(K, Z(q)(o)(K)) = integral K parallel to(center dot, x)parallel to L(q(K))dx. Se show that an upper bound of the form I-1 (K, Z(q)(o)(K)) %26lt;= C-1q(s) root nL(K)(2), with 1/2 %26lt;= s %26lt;= 1, leads to the estimate %26lt;br%26gt;L-n C-2(4)root nlogn/(q)1-2/2, %26lt;br%26gt;where L-n := max{L-K: K is an isotropic convex body in R-n}.

• 出版日期2012-2-1