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Determination of Convex Bodies by Projection Functions
Authors:Christina Bauer
Institution:(1) Zentrum Mathematik, Technische Universität München, D-80290 Munich, Germany; e-mail
Abstract:This paper is concerned with an investigation to what extent a convex body is determined by projection functions. We introduce the notion of convex bodies that are almost determined by their brightness function and give a geometric characterization of these bodies. We further prove that, for i isin ldquo2,...,d–2rdquo, a polytope is determined by its ith projection function, if all of its (i+1)-faces are parallelepipeds. Both results extend work by Gardner and Volccaroniccaron 4].
Keywords:projection function  surface area measure  polytope  
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