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Stability results for sections of convex bodies


Authors: M. Stephen and V. Yaskin
Journal: Trans. Amer. Math. Soc. 369 (2017), 6239-6261
MSC (2010): Primary 52A20; Secondary 42B10
DOI: https://doi.org/10.1090/tran/6854
Published electronically: March 29, 2017
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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown by Makai, Martini, and Ódor that a convex body $ K$, all of whose maximal sections pass through the origin, must be origin-symmetric. We prove a stability version of this result. We also discuss a theorem of Koldobsky and Shane about determination of convex bodies by fractional derivatives of the parallel section function and establish the corresponding stability result.


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Additional Information

M. Stephen
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
Email: mastephe@ualberta.ca

V. Yaskin
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
Email: yaskin@ualberta.ca

DOI: https://doi.org/10.1090/tran/6854
Keywords: Cross-section body, intersection body, stability
Received by editor(s): June 4, 2015
Received by editor(s) in revised form: September 16, 2015
Published electronically: March 29, 2017
Additional Notes: Both authors were partially supported by NSERC
Article copyright: © Copyright 2017 American Mathematical Society

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