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Can I read A Note on the Reduction of the Slicing Problem to Centrally Symmetric Convex Bodies on EtoBox?
A Note on the Reduction of the Slicing Problem to Centrally Symmetric Convex Bodies by Javier Martín-Goñi is a Mathematics article available to read on EtoBox.
What is A Note on the Reduction of the Slicing Problem to Centrally Symmetric Convex Bodies about?
In this paper, we obtain the best possible value of the absolute constant C such that for every isotropic convex body K ⊆ R n the following inequality (which was proved by Klartag and reduces the hyperplane conjecture to centrally symmetric convex bodies) is satisfied:Here L K denotes the isotropic constant of K, g K its covariogram function, which is log-concave, and, for any log-concave function g, K n+2 (g) is a convex body associated to the log-concave function g, which belongs to a uniparametric family introduced by Ball. In order to obtain this inequality, sharp inclusion results between the convex bodies in this family are obtained whenever g satisfies a better type of concavity than the log-concavity, as g K is, indeed 1 n -concave.
Who reads A Note on the Reduction of the Slicing Problem to Centrally Symmetric Convex Bodies?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Javier Martín-Goñi
- Publisher
- Elsevier BV
- Published
- 2023
- Language
- EN
- Field
- Mathematics (Physical Sciences)