Shadows of convex bodies
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- by Keith Ball PDF
- Trans. Amer. Math. Soc. 327 (1991), 891-901 Request permission
Abstract:
It is proved that if $C$ is a convex body in ${\mathbb {R}^n}$ then $C$ has an affine image $\tilde C$ (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 $|K{|^{(n - 1) / n}}$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 327 (1991), 891-901
- MSC: Primary 52A40; Secondary 52A20
- DOI: https://doi.org/10.1090/S0002-9947-1991-1035998-3
- MathSciNet review: 1035998