Slicing convex bodiesbounds for slice area in terms of the bodys covariance Academic Article

Let Q be a zero-symmetric convex set in R N {{mathbf {R}}^N} with volume 1 and covariance matrix V 2 I d N N V^2 mathrm {Id}_{N imes N} . Let P be a K-dimensional vector subspace of R n , K > N {{mathbf {R}}^n},K > N , and let J = N K J = N - K . Then there exist constants C 1 ( J ) {C_1}(J) and C 2 ( J ) {C_2}(J) such that [ V J C 1 ( J ) v o l K ( P Q ) V J C 2