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Let Q be a zero-symmetric convex set in RN with volume I and covariance matrix V2IdN x N. Let P be a K-dimensional vector subspace of R', K < N, and let J = N K. Then there exist constants C1(J) and C2(J) such that V-JCI(J) 1< VOIK(P n Q) < V-JC2(i). The lower bound has applications to Diophantine equations.

Slicing convex bodies—bounds for slice area in terms of the body’s covariance