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Shadows of Convex Bodies

Keith Ball
Transactions of the American Mathematical Society
Vol. 327, No. 2 (Oct., 1991), pp. 891-901
DOI: 10.2307/2001829
Stable URL: http://www.jstor.org/stable/2001829
Page Count: 11
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Shadows of Convex Bodies
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Abstract

It is proved that if C is a convex body in Rn then C has an affine image C̃ (of nonzero volume) so that if P is any 1-codimensional orthogonal projection, $|P\tilde{C}| \geq|\tilde{C}|^{(n-1)/n}$. It is also shown that there is a pathological body, K, all of whose orthogonal projections have volume about $\sqrt n$ times as large as |K|(n-1)/n.

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