Zur Axiomatischen Charakterisierung des Steinerpunktes Konvexer Körper; Berichtigung und Nachtrag

Abstract

The main theorem of a previous paper by H. Hadwiger is wrong, its inductive “proof” only works for the transition from an even to an odd dimension. By requiring covariance under all similarity transformations instead of homothetic transformations alone, we obtain a theorem which is shown to be equivalent to the characterization of Steiner points given by G. C. Shephard, K. A. Schmitt and R. Schneider. For dimensionsn ≦ 3 a new short proof of the latter result is included.