The Flatness Theorem for Nonsymmetric Convex Bodies via the Local Theory of Banach Spaces

Wojciech Banaszczyk, Alexander E. Litvak, Alain Pajor, Stanislaw J. Szarek

Abstract: Let L be a lattice in ℝ n and K a convex body disjoint from L. The classical Flatness Theorem asserts that then w(K, L), the L-width of K, does not exceed some bound, depending only on the dimensio...