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Inequalities between intrinsic volumes

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Abstract

Removing the dependence on dimension of the inequalities between quermassintegrals resulting from the Aleksandrov-Fenchel inequalities leads to universal quadratic inequalities between intrinsic volumes, and to an inequality for the Wills functional. The inequalities correspond to equations which hold in the polytope algebra.

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References

  1. Aleksandrov, A. D.: Zur Theorie gemischter Volumina von konvexen Körpern; II: Neue Ungleichungen zwischen den gemischten Volumina und ihre Anwendungen. Matem. Sb. SSSR2, 1205–1238 (1937).

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  2. Bonnesen, T., Fenchel, W.: Theorie der konvexen Körper. Berlin: Springer. 1934.

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  3. Hadwiger, H.: Vorlesungen über Inhalt, Oberfläche und Isoperimetrie. Berlin-Göttingen-Heidelberg: Springer. 1934.

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  4. Hadwiger, H.: Das Wills'sche Funktional. Mh. Math.79, 213–221 (1975).

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  5. Leichweiss, K.: Konvexe Mengen. Berlin-Heidelberg-New York: Springer. 1979.

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  6. McMullen, P.: Non-linear angle-sum relations for polyhedral cones and polytopes. Math. Proc. Cambridge Phil. Soc.78, 247–261 (1975).

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  7. McMullen, P.: The polytope algebra. Adv. Math.78, 76–130 (1989).

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  8. Wills, J. M.: Zur Gitterpunktanzahl konvexer Mengen. Elem. Math.28, 57–63 (1973).

    Google Scholar 

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McMullen, P. Inequalities between intrinsic volumes. Monatshefte für Mathematik 111, 47–53 (1991). https://doi.org/10.1007/BF01299276

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