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A classification of some unit Lorentz balls as non-intersection bodies


Author: Patrick Spencer
Journal: Proc. Amer. Math. Soc. 143 (2015), 1211-1220
MSC (2010): Primary 52A20; Secondary 42A38, 42A82, 46F12
DOI: https://doi.org/10.1090/S0002-9939-2014-11821-1
Published electronically: November 4, 2014
MathSciNet review: 3293736
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Abstract: We show that the unit ball of the $ n$-dimensional Lorentz space $ \ell _{w,q}^n$ is not an intersection body for $ q>2$ and $ n\ge 5$.


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Additional Information

Patrick Spencer
Affiliation: Department of Mathematics, 202 Mathematical Sciences Building, University of Missouri, Columbia, Missouri 65211
Email: patrick.spencer@mail.mizzou.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-11821-1
Keywords: Lorentz space, intersection bodies
Received by editor(s): December 2, 2011
Received by editor(s) in revised form: April 5, 2012, and April 17, 2012
Published electronically: November 4, 2014
Additional Notes: The author would like to thank Alexander Koldobsky for all his guidance and support throughout this paper.
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2014 American Mathematical Society