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Isoperimetric inequalities and identities fork-dimensional cross-sections of convex bodies

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References

  1. Bertrand, J.L.F.: J. Liouville7, 215–216 (1842)

    Google Scholar 

  2. Blaschke, W.: Über affine Geometrie. Leipz. Ber.21, 330–335 (1918)

    Google Scholar 

  3. Burago, Y.D., Zalgaller, V.A.: Geometric inequlities. Berlin Heidelberg New York: Springer 1988

    Google Scholar 

  4. Burton, G.R.: Sections of convex bodies. J. Lond. Math. Soc.12, 331–336 (1975/76)

    Google Scholar 

  5. Busemann, H.: Volume in terms of concurrent cross-sections. Pac. J. Math.3, 1–12 (1953)

    Google Scholar 

  6. Busemann, H.: The geometry of geodesics. New York: Academic Press 1955

    Google Scholar 

  7. Federer, H.: Geometric measure theory. Berlin Heidelberg New York: Springer 1969

    Google Scholar 

  8. Furstenberg, H., Tzkoni, I.: Spherical harmonics and integral geometry. Isr. J. Math.10, 327–338 (1971)

    Google Scholar 

  9. Grinberg, E.: Inst. Haut. Etud. Sci. Preprint IHES/M/86/28 (1986)

  10. Guggenheimer, H.: Global and local convexity, applicable geometry. Huntington, NY: Kreiger 1977

    Google Scholar 

  11. Guggenheimer, H.: A formula of Furstenberg-Tzkoni type. Isr. J. Math.14, 281–282 (1973)

    Google Scholar 

  12. Lutwak, E.: Inequalities for Hadwiger's harmonic quermassintegrals. Math. Ann.280, 165–175 (1988)

    Google Scholar 

  13. Lutwak, E.: Intersection bodies and dual mixed volumes. Adv. Math.71, 232–261 (1988).

    Google Scholar 

  14. Lutwak, E.: A general isepiphanic inequality. Proc. Am. Math. Soc.90, 415–421 (1984)

    Google Scholar 

  15. Miles, R.E.: A simple derivation of a formula of Furstenberg and Tzkoni. Adv. Appl. Probab.3, 353–382 (1971); Isr. J. Math.14, 278–280 (1973)

    Google Scholar 

  16. Petty, C.M.: Isoperimetric problems, in: Proc. Conf. Convexity and Combinatorial Geometry (U. Oklahoma, 1971), pp. 26–41 (1972)

  17. Santaló, L.: Integral geometry probability. Encyclopedia of Mathematics Reading, Mass.: Addison-Wesley 1976

    Google Scholar 

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  1. Temple University, 19122, Philadelphia, PA, USA

    Eric L. Grinberg

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  1. Eric L. Grinberg
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Supported in part by a grant from the National Science foundation

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Grinberg, E.L. Isoperimetric inequalities and identities fork-dimensional cross-sections of convex bodies. Math. Ann. 291, 75–86 (1991). https://doi.org/10.1007/BF01445191

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  • DOI: https://doi.org/10.1007/BF01445191

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