Abstract
LetK be a convex body in (n+1)-dimensional Euclidean space En+1. The set Σ(K) of all support-elements ofK is uniquely determined by the semiaxis-function a(u). First part of this note contains an explicit specification of the support-elements by means of a(u), and in the second part we give necessary and sufficient conditions which characterize a function a(u) as semiaxis-function of a closed convex subset of En+1.
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Literatur
BAUM, D.: Zur analytischen Darstellung des Randes konvexer Körper I. Halbachsenfunktion und Scheitelfläche. manuscripta math. 9, 113–141 (1973).
LEICHTWEISS, K.: Über eine analytische Darstellung des Randes konvexer Körper. Arch. Math. 16, 300–319 (1965).
VALENTINE, F. A.: Konvexe Mengen, 1. Aufl. Manmheim: Bibliographisches Institut 1968.
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Baum, D. Zur Analytischen Darstellung des Ranges Konvexer Körper Durch Stützhyperboloide. Manuscripta Math 9, 307–322 (1973). https://doi.org/10.1007/BF01343872
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DOI: https://doi.org/10.1007/BF01343872