Open Access

Inequalities for dual affine quermassintegrals

Journal of Inequalities and Applications20062006:50181

https://doi.org/10.1155/JIA/2006/50181

Received: 18 April 2005

Accepted: 8 November 2005

Published: 14 May 2006

Abstract

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.

[12345678910]

Authors’ Affiliations

(1)
Department of Mathematics, Shanghai University

References

  1. Bonnesen T, Fenchel W: Theorie der konvexen Körper. Springer, Berlin; 1934.MATHView ArticleGoogle Scholar
  2. Federer H: Geometric Measure Theory, Die Grundlehren der mathematischen Wissenschaften. Volume 153. Springer, New York; 1969:xiv+676.Google Scholar
  3. Gardner RJ: Geometric Tomography, Encyclopedia of Mathematics and Its Applications. Volume 58. Cambridge University Press, Cambridge; 1995:xvi+424.Google Scholar
  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/22.5.478MATHMathSciNetView ArticleGoogle Scholar
  5. Leichtweiss K: Konvexe Mengen. Springer, Berlin; 1980:330 pp. (loose errata).View ArticleGoogle Scholar
  6. Lutwak E: Dual mixed volumes. Pacific Journal of Mathematics 1975,58(2):531–538.MATHMathSciNetView ArticleGoogle Scholar
  7. Lutwak E: A general isepiphanic inequality. Proceedings of the American Mathematical Society 1984,90(3):415–421. 10.1090/S0002-9939-1984-0728360-3MATHMathSciNetView ArticleGoogle Scholar
  8. Lutwak E: Inequalities for Hadwiger's harmonic quermassintegrals. Mathematische Annalen 1988,280(1):165–175. 10.1007/BF01474188MATHMathSciNetView ArticleGoogle Scholar
  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. 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

Copyright

© Y. Jun and L. Gangsong. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.