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arXiv · 1505.05817

Counterexamples Related to Rotations of Shadows of Convex Bodies

M. Angeles Alfonseca·Michelle Cordier
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Abstract

We construct examples of two convex bodies $K,L$ in $\mathbb{R}^n$, such that every projection of $K$ onto a $(n-1)$-dimensional subspace can be rotated to be contained in the corresponding projection of $L$, but $K$ itself cannot be rotated to be contained in $L$. We also find necessary conditions on $K$ and $L$ to ensure that $K$ can be rotated to be contained in $L$ if all the $(n-1)$-dimensional projections have this property.

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M. Angeles Alfonseca, Michelle Cordier. 2015-05-21. Counterexamples Related to Rotations of Shadows of Convex Bodies. https://arxiv.org/abs/1505.05817

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