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Shaken Rogers's Theorem for Homothetic Sections

Published online by Cambridge University Press:  20 November 2018

J. Jerónimo-Castro
Affiliation:
Instituto de Matemáticas, UNAM, Ciudad Universitaria, C.P. 04510, México, D.F., andFacultad de Matemáticas, Acapulco, Universidad Autónoma de Guerrero e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]
L. Montejano
Affiliation:
Instituto de Matemáticas, UNAM, Ciudad Universitaria, C.P. 04510, México, D.F., andFacultad de Matemáticas, Acapulco, Universidad Autónoma de Guerrero e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]
E. Morales-Amaya
Affiliation:
Instituto de Matemáticas, UNAM, Ciudad Universitaria, C.P. 04510, México, D.F., andFacultad de Matemáticas, Acapulco, Universidad Autónoma de Guerrero e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2009

References

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