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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On bodies with congruent sections by cones or non-central planes


Author: N. Zhang
Journal: Trans. Amer. Math. Soc. 370 (2018), 8739-8756
MSC (2010): Primary 52A20, 52A38
DOI: https://doi.org/10.1090/tran/7395
Published electronically: September 13, 2018
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Abstract: Let $ K$ and $ L$ be two convex bodies in $ \mathbb{R}^3$, such that their sections by cones $ \{x\in \mathbb{R}^3:x\cdot \xi =t\vert x\vert\}$ or non-central planes with a fixed distance from the origin are directly congruent. We prove that if their boundaries are of class $ C^2$, then $ K$ and $ L$ coincide.


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Additional Information

N. Zhang
Affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, People’s Republic of China
Email: nzhang2@ualberta.ca

DOI: https://doi.org/10.1090/tran/7395
Keywords: Convex body, congruent sections, unique determination
Received by editor(s): May 8, 2017
Received by editor(s) in revised form: July 22, 2017
Published electronically: September 13, 2018
Article copyright: © Copyright 2018 American Mathematical Society

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