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Convex bodies and convexity on Grassmann cones

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References

  1. Alexandroff, P., andH. Hopf: Topologie I, Berlin 1935, (reprinted Ann Arbor, Mich. 1945).

  2. Barthel, W.: Zum Busemannschen und Brunn-Minkowskischen Satz. Math. Z.70, 407–420 (1959).

    Google Scholar 

  3. Bonnesen, T., andW. Fenchel: Theorie der konvexen Körper. Berlin 1934 and New York 1948.

  4. Bourbaki, N.: Algèbre Multilinéaire, Éléments de Math. I, Livre II Chap. 3. Paris 1958.

  5. Busemann, H.: Convex surfaces. New York 1958.

  6. —— Area in affine spaces III. Rend. Circ. Mat. Palermo, Ser. II,9, 226–242 (1960).

    Google Scholar 

  7. —— Convexity on Grassmann manifolds. Enseign. Math.7, 139–152 (1961).

    Google Scholar 

  8. ——, andE. G. Strauss: Area and normality. Pacific J. Math.10, 35–72 (1960).

    Google Scholar 

  9. Cartan, É.: Leçons sur la géometrie des espaces de Riemann. 2nd Ed. Paris 1946.

  10. Coxeter, H. S. M.: Regular polytopes. New York 1948.

  11. Dowker, C. H.: On minimum circumscribed polygons. Bull. Amer. Math. Soc.50, 120–122 (1944).

    Google Scholar 

  12. Hadwiger, H.: Vorlesungen über Inhalt, Oberfläche und Isoperimetrie. Berlin-Göttingen-Heidelberg: Springer 1957.

    Google Scholar 

  13. Petkantschin, B.: Integralgeometrie 6, Zusammenhänge zwischen den Dichten der linearen Unterräume imn-dimensionalen Raum. Abhandl. Math. Seminar Hamburg. Univ.11, 249–310 (1936).

    Google Scholar 

  14. Shephard, G. C.: Inequalities between mixed volumes of convex sets. Mathematika7, 125–138 (1960).

    Google Scholar 

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Authors and Affiliations

  1. Los Angeles

    H. Busemann

  2. Mainz

    G. Ewald

  3. Birmingham, England

    G. C. Shephard

Authors
  1. H. Busemann
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  2. G. Ewald
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  3. G. C. Shephard
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Additional information

This work was supported by a grant from the National Science Foundation, U.S.A.

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Busemann, H., Ewald, G. & Shephard, G.C. Convex bodies and convexity on Grassmann cones. Math. Ann. 151, 1–41 (1963). https://doi.org/10.1007/BF01343323

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  • DOI: https://doi.org/10.1007/BF01343323

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