[Banach] Abstract of a paper by Apostolos Giannopoulos, Grigoris Paouris, and Beatrice-Helen Vritsiou

This is an announcement for the paper "A remark on the slicing problem" by Apostolos Giannopoulos, Grigoris Paouris, and Beatrice-Helen Vritsiou.

Abstract: 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))=\int_K ||< : ,x> ||_{L_q(K)}dx. We show that an upper bound of the form I_1(K,Z_q^o(K))\leq C_1q^s\sqrt{n}L_K^2, with 1/2\leq s\leq 1, leads to the estimate L_n\leq \frac{C_2\sqrt[4]{n}log(n)} {q^{(1-s)/2}}, where L_n:= max {L_K : K is an isotropic convex body in R^n}.

Archive classification: math.FA math.MG

Mathematics Subject Classification: 52A23, 46B06, 52A40

Remarks: 24 pages

Submitted from: bevritsi@math.uoa.gr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1107.4527

or

http://arXiv.org/abs/1107.4527