APM  Vol.3 No.1 , January 2013
The Brunn-Minkowski Inequalities for Centroid Body
Author(s) Jun Yuan*, Lingzhi Zhao
ABSTRACT
In [1], the authors established the Brunn-Minkowski inequality for centroid body. In this paper, we give an isolate form and volume difference of it, respectively. Both of these results are strength versions of the original.

Cite this paper
J. Yuan and L. Zhao, "The Brunn-Minkowski Inequalities for Centroid Body," Advances in Pure Mathematics, Vol. 3 No. 1, 2013, pp. 105-108. doi: 10.4236/apm.2013.31013.
References
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[3]   K. Leichtwei, “Affine Geometry of Convex Bodies,” J. A. Barth, Heidelberg, 1998.

[4]   R. Schneider, “Convex Bodies: The Brunn-Minkowski Theory,” Cambridge University Press, Cambridge, 1993. doi:10.1017/CBO9780511526282

[5]   R. J. Gardner, “Geometric Tomography,” Cambridge University Press, Cambridge, 1995.

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[8]   E. Lutwak, “The Brunn-Minkowski-Firey Theory I: Mixed Volumes and the Minkowski Problem,” Journal of Differential Geometry, Vol. 38, 1993, pp. 131-150.

[9]   A. D. Aleksandrov, “Zur Theorie der Gemischten Volumina von Konvexen K?rpern, I. Verallgemeinerung einiger Begriffe der Theorie der Konvexen Korpern,” Matematicheskii Sbornik, Vol. 2, 1937, pp. 947-972.

[10]   W. Fenchel and B. Jessen, “Mengenfunktionen und Konvexe K?rpern,” Danske Videnskabernes Selskab. Matematisk-Fysiske Meddelelser, Vol. 16, 1938, p. 3.

[11]   R. J. Gardner, “The Brunn-Minkowski Inequality,” Bulletin of the American Mathematical Society, Vol. 39, No. 3, 2002, pp. 355-405. doi:10.1090/S0273-0979-02-00941-2

[12]   E. F. Beckenbach and R. Bellman, “Inequalities,” Springer, Berlin, 1961. doi:10.1007/978-3-642-64971-4

 
 
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