Cone-volume measure and stability
  We show that the cone-volume measure of a convex body with centroid at the origin satisfies the subspace concentration condition. This implies, among others, a conjectured best possible inequality for the $\mathrm{U}$-functional of a convex body. For both results we provide stronger versions in the sense of stability inequalities. 
K\'aroly J. B\"or\"oczky and Martin Henk
math.MG math.DG