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Inequalities for dual affine quermassintegrals


For star bodies, the dual affine quermassintegrals were introduced and studied in several papers. The aim of this paper is to study them further. In this paper, some inequalities for dual affine quermassintegrals are established, such as the Minkowski inequality, the dual Brunn-Minkowski inequality, and the Blaschke-Santaló inequality.



  1. 1.

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

    Google Scholar 

  2. 2.

    Federer H: Geometric Measure Theory, Die Grundlehren der mathematischen Wissenschaften. Volume 153. Springer, New York; 1969:xiv+676.

    Google Scholar 

  3. 3.

    Gardner RJ: Geometric Tomography, Encyclopedia of Mathematics and Its Applications. Volume 58. Cambridge University Press, Cambridge; 1995:xvi+424.

    Google Scholar 

  4. 4.

    Grinberg EL: Isoperimetric inequalities and identities for-dimensional cross-sections of a convex bodies. London Mathematical Society 1990, 22: 478–484. 10.1112/blms/22.5.478

    MATH  MathSciNet  Article  Google Scholar 

  5. 5.

    Leichtweiss K: Konvexe Mengen. Springer, Berlin; 1980:330 pp. (loose errata).

    Google Scholar 

  6. 6.

    Lutwak E: Dual mixed volumes. Pacific Journal of Mathematics 1975,58(2):531–538.

    MATH  MathSciNet  Article  Google Scholar 

  7. 7.

    Lutwak E: A general isepiphanic inequality. Proceedings of the American Mathematical Society 1984,90(3):415–421. 10.1090/S0002-9939-1984-0728360-3

    MATH  MathSciNet  Article  Google Scholar 

  8. 8.

    Lutwak E: Inequalities for Hadwiger's harmonic quermassintegrals. Mathematische Annalen 1988,280(1):165–175. 10.1007/BF01474188

    MATH  MathSciNet  Article  Google Scholar 

  9. 9.

    Santaló LA: Integral Geometry and Geometric Probability, Encyclopedia of Mathematics and Its Applications. Volume 1. Addison-Wesley, Massachusetts; 1976:xvii+404.

    Google Scholar 

  10. 10.

    Schneider R: Convex Bodies: the Brunn-Minkowski Theory, Encyclopedia of Mathematics and Its Applications. Volume 44. Cambridge University Press, Cambridge; 1993:xiv+490.

    Google Scholar 

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Correspondence to Yuan Jun.

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Jun, Y., Gangsong, L. Inequalities for dual affine quermassintegrals. J Inequal Appl 2006, 50181 (2006).

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  • Minkowski Inequality
  • Star Body
  • Dual Affine