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Über einige Eindeutigkeitssätze für konvexe Körper

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Abstract

In this note,three unity theorems for compact convex bodies with interior points in euclidean space Rn up to translation resp. dilatation resp. (perspective) affinity are formulated.The first two of them are in a certain sense generalizations of well known theorems of K.VPOSS ans A.AEPPLI concerning convex hypersurfaces.All of them suppose relations of the supporting hyperplanes in corresponding points of two given convex bodies.Their proofs use the main theorem of calculus in the Lebesgue theory, and they have applications in the discussion of equality in some fundamental inequalities of the theory of convex bodies.

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  1. Mathematisches Institut B der Universität Stuttgart, Pfaffenwaldring 57, 7000, Stuttgart 80

    Kurt Leichtweiss

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  1. Kurt Leichtweiss
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Leichtweiss, K. Über einige Eindeutigkeitssätze für konvexe Körper. Manuscripta Math 23, 213–245 (1978). https://doi.org/10.1007/BF01171751

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