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  • 1 Faculty of Mathematics, University of Technology Chemnitz 09107 Chemnitz, Germany 09107 Chemnitz, Germany
  • 2 Department of Mathematics, University of Houston-Clear Lake Houston, TX 77058 USA Houston, TX 77058 USA
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The purpose of this paper is to establish extremal values for inner and outer radii of the unit ball of a Minkowski space for the Holmes--Thompson and Busemann measures. Furthermore, we confirm a conjecture of C. A. Rogers and G. C. Shephard on ellipsoids.