Verification of polytopes by brightness functions
Author:
Rolf Schneider
Journal:
Proc. Amer. Math. Soc. 137 (2009), 3899-3903
MSC (2000):
Primary 52A20; Secondary 52A21
DOI:
https://doi.org/10.1090/S0002-9939-09-10041-2
Published electronically:
June 25, 2009
MathSciNet review:
2529898
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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:
https://doi.org/10.1090/S0002-9939-09-10041-2
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.
