1. CMB 2009 (vol 52 pp. 403)
|Shaken Rogers's Theorem for Homothetic Sections |
We shall prove the following shaken Rogers's theorem for homothetic sections: Let $K$ and $L$ be strictly convex bodies and suppose that for every plane $H$ through the origin we can choose continuously sections of $K $ and $L$, parallel to $H$, which are directly homothetic. Then $K$ and $L$ are directly homothetic.
Keywords:convex bodies, homothetic bodies, sections and projections, Rogers's Theorem