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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Verification of polytopes by brightness functions


Author: Rolf Schneider
Journal: Proc. Amer. Math. Soc. 137 (2009), 3899-3903
MSC (2000): Primary 52A20; Secondary 52A21
Published electronically: June 25, 2009
MathSciNet review: 2529898
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Abstract: We show that in the class of origin-centered convex bodies in Euclidean space of dimension at least three, a polytope is uniquely determined by its brigthness function in a suitably chosen, but very small set of directions.


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Additional Information

Rolf Schneider
Affiliation: Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstrasse 1, D-79104 Freiburg i. Br., Germany
Email: rolf.schneider@math.uni-freiburg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10041-2
PII: S 0002-9939(09)10041-2
Keywords: Convex body, projection volume, brightness function, Aleksandrov's projection theorem, geometric tomography
Received by editor(s): October 26, 2008
Published electronically: June 25, 2009
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.