Centroid bodies and the logarithmic Laplace transform - A unified approach (Q652428)

The paper unifies and slightly improves several bounds on the isotropic constant of high-dimensional convex bodies; in particular, a~linear dependence on the body's \(\psi_2\) constant is obtained. Along the way, some new bounds on the volume of \( L_p\)-centroid bodies are presented and yet another equivalent formulation of Bourgain's hyperplane conjecture is given. The method used is a~combination of the \(L_p\)-centroid body technique of Paouris and the logarithmic Laplace transform technique (using the logarithmic Laplace transform) of the first named author.