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# Shaken Rogers's Theorem for Homothetic Sections

Published:2009-09-01
Printed: Sep 2009
• J. Jerónimo-Castro
• L. Montejano
• E. Morales-Amaya
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## Abstract

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
 MSC Classifications: 52A15 - Convex sets in $3$ dimensions (including convex surfaces) [See also 53A05, 53C45]

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