Abstract

This work comprises a study of the behaviour of projection functions of convex bodies considered as functions defined on Grassmannian manifolds. We show that the behaviour in the case of higher rank manifolds is often very different from the rank 1 case. We also study the images of projection functions under Radon transforms. If X is an n-dimensional normed space, and d denotes the Banach-Mazur distance, then d(X, l ∞ n ) ≤ cn 5/6.

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