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