Skip to main content

Dual affine isoperimetric inequalities

Abstract

We establish some inequalities for the dual-centroid bodies which are the dual forms of the results by Lutwak, Yang, and Zhang. Further, we establish a Brunn-Minkowski-type inequality for the polar of dual-centroid bodies.

[12345678910]

References

  1. 1.

    Campi S, Gronchi P: The-Busemann-Petty centroid inequality. Advances in Mathematics 2002,167(1):128–141. 10.1006/aima.2001.2036

    MATH  MathSciNet  Article  Google Scholar 

  2. 2.

    Firey WmJ: -means of convex bodies. Mathematica Scandinavica 1962, 10: 17–24.

    MATH  MathSciNet  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.

    Lutwak E: The Brunn-Minkowski-Firey theory. I. Mixed volumes and the Minkowski problem. Journal of Differential Geometry 1993,38(1):131–150.

    MATH  MathSciNet  Google Scholar 

  5. 5.

    Lutwak E, Yang D, Zhang G: affine isoperimetric inequalities. Journal of Differential Geometry 2000,56(1):111–132.

    MATH  MathSciNet  Google Scholar 

  6. 6.

    Lutwak E, Yang D, Zhang G: A new ellipsoid associated with convex bodies. Duke Mathematical Journal 2000,104(3):375–390. 10.1215/S0012-7094-00-10432-2

    MATH  MathSciNet  Article  Google Scholar 

  7. 7.

    Lutwak E, Yang D, Zhang G: John ellipsoids. Proceedings of the London Mathematical Society. Third Series 2005,90(2):497–520. 10.1112/S0024611504014996

    MATH  MathSciNet  Article  Google Scholar 

  8. 8.

    Lutwak E, Zhang G: Blaschke-Santaló inequalities. Journal of Differential Geometry 1997,47(1):1–16.

    MATH  MathSciNet  Google Scholar 

  9. 9.

    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 

  10. 10.

    Thompson AC: Minkowski Geometry, Encyclopedia of Mathematics and Its Applications. Volume 63. Cambridge University Press, Cambridge; 1996:xvi+346.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Si Lin.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lin, S., Bin, X. & Wuyang, Y. Dual affine isoperimetric inequalities. J Inequal Appl 2006, 84825 (2006). https://doi.org/10.1155/JIA/2006/84825

Download citation

Keywords

  • Isoperimetric Inequality
  • Dual Form
  • Centroid Body
  • Affine Isoperimetric Inequality
\