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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
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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.


References [Enhancements On Off] (What's this?)

  • 1. Gardner, R.J., Geometric Tomography. Encyclopedia of Mathematics and its Applications, vol. 58, second ed., Cambridge University Press, Cambridge, 2006. MR 2251886 (2007i:52010)
  • 2. Grinberg, E.L., Quinto, E.T., Analytic continuation of convex bodies and Funk's characterization of the sphere. Pacific J. Math 201 (2001), 309-322. MR 1875896 (2003a:52005)
  • 3. Schneider, R., On the projections of a convex polytope. Pacific J. Math. 32 (1970), 799-803. MR 0267461 (42:2363)
  • 4. Schneider, R., Convex Bodies: The Brunn-Minkowski Theory. Encyclopedia of Mathematics and its Applications, vol. 44. Cambridge University Press, Cambridge, 1993. MR 1216521 (94d:52007)
  • 5. Schneider, R., Weil, W., Über die Bestimmung eines konvexen Körpers durch die Inhalte seiner Projektionen. Math. Z. 116 (1970), 338-348. MR 0283692 (44:922)

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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.

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