TY - JOUR
T1 - Centroid bodies and the logarithmic Laplace transform - A unified approach
AU - Klartag, Bo'az
AU - Milman, Emanuel
N1 - Funding Information:
* Corresponding author. E-mail addresses: klartagb@tau.ac.il (B. Klartag), emilman@tx.technion.ac.il (E. Milman). 1 Supported in part by the Israel Science Foundation and by a Marie Curie Reintegration Grant from the Commission of the European Communities. 2 Supported by ISF, GIF and the Taub Foundation (Landau Fellow).
PY - 2012/1/1
Y1 - 2012/1/1
N2 - We unify and slightly improve several bounds on the isotropic constant of high-dimensional convex bodies; in particular, a linear dependence on the body's ψ2 constant is obtained. Along the way, we present some new bounds on the volume of Lp-centroid bodies and yet another equivalent formulation of Bourgain's hyperplane conjecture. Our method is a combination of the Lp-centroid body technique of Paouris and the logarithmic Laplace transform technique of the first named author.
AB - We unify and slightly improve several bounds on the isotropic constant of high-dimensional convex bodies; in particular, a linear dependence on the body's ψ2 constant is obtained. Along the way, we present some new bounds on the volume of Lp-centroid bodies and yet another equivalent formulation of Bourgain's hyperplane conjecture. Our method is a combination of the Lp-centroid body technique of Paouris and the logarithmic Laplace transform technique of the first named author.
KW - Hyperplane conjecture
KW - Logarithmic Laplace transform
KW - Psi-2
UR - http://www.scopus.com/inward/record.url?scp=80955142661&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2011.09.003
DO - 10.1016/j.jfa.2011.09.003
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AN - SCOPUS:80955142661
SN - 0022-1236
VL - 262
SP - 10
EP - 34
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -