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Verification of polytopes by brightness functions
Author(s):
Rolf
Schneider
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3899-3903.
MSC (2000):
Primary 52A20;
Secondary 52A21
Posted:
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.
References:
-
- 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:
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
Posted:
June 25, 2009
Communicated by:
Jon G. Wolfson
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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