The (B) conjecture for the Gaussian measure of dilates of symmetric convex sets and related problems

Abstract : We show that given a symmetric convex set K subset of R-d, the function t-->gamma(e(l) K) is loa-concave on R, where gamma denotes the standard d-dimensional Gaussian measure. We also comment on the extension of this property to unconditional log-concave measures and sets, and on the complex case. (C) 2003 Elsevier Inc. All rights reserved.