### arXiv:math/9201204 [math.MG]AbstractReferencesReviewsResources

#### Shadows of convex bodies

Published 1989-10-26Version 1

It is proved that if $C$ is a convex body in ${\Bbb R}^n$ then $C$ has an affine image $\widetilde C$ (of non-zero volume) so that if $P$ is any 1-codimensional orthogonal projection, $$|P\widetilde C| \ge |\widetilde C|^{n-1\over n}.$$ 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 $|K|^{n-1\over n}$.

arXiv:1604.05351 [math.MG] (Published 2016-04-12)

On the volume of sections of a convex body by cones

Affine diameters of convex bodies

Thrifty approximations of convex bodies by polytopes