Taiwanese Journal of Mathematics

The Dual Log-Brunn-Minkowski Inequalities

Wei Wang and Lijuan Liu

Full-text: Open access

Abstract

In this article, we establish the dual log-Brunn-Minkowski inequality and the dual log-Minkowski inequality. Moreover, the equivalence between the dual log-Brunn-Minkowski inequality and the dual log-Minkowski inequality is demonstrated.

Article information

Source
Taiwanese J. Math., Volume 20, Number 4 (2016), 909-919.

Dates
First available in Project Euclid: 1 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1498874497

Digital Object Identifier
doi:10.11650/tjm.20.2016.6323

Mathematical Reviews number (MathSciNet)
MR3535680

Zentralblatt MATH identifier
1357.52011

Subjects
Primary: 52A40: Inequalities and extremum problems 53A15: Affine differential geometry

Keywords
star body radial function log radial sum dual Brunn-Minkowski inequality dual Minkowski inequality

Citation

Wang, Wei; Liu, Lijuan. The Dual Log-Brunn-Minkowski Inequalities. Taiwanese J. Math. 20 (2016), no. 4, 909--919. doi:10.11650/tjm.20.2016.6323. https://projecteuclid.org/euclid.twjm/1498874497


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References

  • K. J. Böröczky, E. Lutwak, D. Yang and G. Zhang, The log-Brunn-Minkowski inequality, Adv. Math. 231 (2012), no. 3-4, 1974–1997.
  • W. J. Firey, $p$-means of convex bodies, Math. Scand. 10 (1962), 17–24.
  • R. J. Gardner, The Brunn-Minkowski inequality, Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 3, 355–405.
  • ––––, Geometric Tomography, Second edition, Encyclopedia of Mathematics and its Applications, 58, Cambridge University Press, Cambridge, 2006.
  • P. M. Gruber, Convex and Discrete Geometry, Grundlehren der Mathematischen Wissenschaften, 336, Springer, Berlin, 2007.
  • G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Reprint of the 1952 edition, Cambridge mathematical Library, Cambridge University Press, Cambridge, 1988.
  • E. Lutwak, Dual mixed volumes, Pacific J. Math. 58 (1975), no. 2, 531–538.
  • ––––, The Brunn-Minkowski-Firey theory I: Mixed volumes and the Minkowski problem, J. Differential Geom. 38 (1993), no. 1, 131–150.
  • R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Encyclopedia of Mathematics and its Applications, 44, Cambridge University Press, Cambridge, 1993.