A remark on the slicing problem
| Autor: | Grigoris Paouris, Apostolos Giannopoulos, Beatrice-Helen Vritsiou |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
010102 general mathematics
Isotropy Mathematics::Rings and Algebras Metric Geometry (math.MG) 52A23 46B06 52A40 Isotropic body Isotropic constant Binary logarithm 01 natural sciences Upper and lower bounds Slicing Functional Analysis (math.FA) 010101 applied mathematics Combinatorics Reduction (complexity) Mathematics - Functional Analysis Mathematics - Metric Geometry Convex body FOS: Mathematics Centroid bodies 0101 mathematics Analysis Mathematics |
| Zdroj: | Journal of Functional Analysis. 262(3):1062-1086 |
| ISSN: | 0022-1236 |
| DOI: | 10.1016/j.jfa.2011.10.011 |
| Popis: | 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}. 24 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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