Symmetrization and Isotropic Constants of Convex Bodies

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Concentration of mass on convex bodies (2006, background): “However, it was observed in [14] that the general case follows easily.”
On convex perturbations with a bounded isotropic constant (2006, background): “A reduction of the problem to the case of bodies with a bounded volume ratio appears in [7, 8].”
Reverse Brunn–Minkowski and reverse entropy power inequalities for convex measures (2011, background): “in isotropic position is equivalent to the hyperplane conjecture ([18]).”
Centroid Bodies and the Logarithmic Laplace Transform - A Unified Approach (2011, unknown): “This question is usually referred to as the slicing problem or hyperplane conjecture, see Milman and Pajor [21] for many of its equivalent formulations and for further background.”