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Determination of convex bodies by their brightness functions

Part of:General convexity

Published online by Cambridge University Press:  26 February 2010

R. J. Gardner and
A. Volčič
R. J. Gardner
Affiliation:
Department of Mathematics, Western Washington University, Bellingham, WA 98225-9063, U.S.A.
A. Volčič
Affiliation:
Dipartimento di Scienze Matematiche, Universitá degli Studi di Trieste, 34100 Trieste, Italy.
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Abstract

It is shown that a convex body is determined uniquely among all convex bodies by the volumes of its projections onto all hyperplanes through the origin if and only if it is a parallelotope.

MSC classification

Secondary:52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)

Information

Type
Research Article
Information
Mathematika , Volume 40 , Issue 2 , December 1993, pp. 161 - 168
Copyright
Copyright © University College London 1993

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