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On steiner points of convex bodies

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Abstract

Ifs is a mapping from the set of all convex bodies in Euclidean spaceE d toE d which is additive (in the sense of Minkowski), equivariant with respect to proper motions, and continuous, thens(K) is the Steiner point of the convex bodyK.

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References

  1. C. Berg,Abstract Steiner points for convex polytopes, (to appear).

  2. W. Blaschke,Über affine Geometrie. IX. Verschiedene Bemerkungen und Aufgaben, Ber. Verh. Sächs. Akad. Leipzig69 (1917), 412–420.

    Google Scholar 

  3. T. Bonnesen and W. Fenchel,Theorie der konvexen Körper, Springer, Berlin, 1934.

    MATH  Google Scholar 

  4. R. R. Coifman and G. Weiss,Representations of compact groups and spherical harmonics, Enseignement Math.14 (1968), 121–173.

    MATH  MathSciNet  Google Scholar 

  5. H. Flanders,The Steiner point of closed hypersurfaces, Mathematika,13 (1966), 181–188.

    MathSciNet  Google Scholar 

  6. B. Grünbaum,Measures of symmetry for convex sets, Proc. Symposia Pure Math., Vol. VII, Convexity. Amer. Math. Soc., Providence, 233–270, 1963.

    Google Scholar 

  7. B. Grünbaum,Convex polytopes, John Wiley and Sons, London-New York-Sydney, 1967.

    MATH  Google Scholar 

  8. H. Hadwiger,Zur axiomatischen Charakterisierung des Steinerpunktes konvexer Körper, Israel J. Math.7 (1969), 168–176.

    Article  MathSciNet  Google Scholar 

  9. H. Hadwiger,Zur axiomatischen Charakterisierung des Steinerpunktes konvexer Körper; Berichtigung und Nachtrag, Israel J. Math. (to appear).

  10. W. Meyer,A uniqueness property of the Steiner point, Pacific J. Math. (to appear).

  11. C. Müller,Spherical harmonics, Lecture Notes in Math.17, Springer, Berlin-Heidelberg-New York, 1966.

    MATH  Google Scholar 

  12. G. T. Sallee,A valuation property of Steiner points, Mathematika13 (1966), 76–82.

    Article  MathSciNet  MATH  Google Scholar 

  13. K. A. Schmitt,Kennzeichnung des Steinerpunktes konvexer Körper, Math. Z.105 (1968), 387–392.

    Article  MATH  MathSciNet  Google Scholar 

  14. R. Schneider,Functions on a sphere with vanishing integrals over certain subspheres, J. Math. Anal. Appl.26 (1969), 381–384.

    Article  MATH  MathSciNet  Google Scholar 

  15. G. C. Shephard,The Steiner point of a convex polytope, Canad. J. Math.18 (1966), 1294–1300.

    MATH  MathSciNet  Google Scholar 

  16. G. C. Shephard,A uniqueness theorem for the Steiner point of a convex region, J. London Math. Soc.43 (1968), 439–444.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Deutschland Institut für Reine Mathematik, Universität Frankfurt, Germany

    Rolf Schneider

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  1. Rolf Schneider
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Schneider, R. On steiner points of convex bodies. Israel J. Math. 9, 241–249 (1971). https://doi.org/10.1007/BF02771589

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  • DOI: https://doi.org/10.1007/BF02771589

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