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http://dx.doi.org/10.4134/JKMS.2010.47.2.277

MIXED CHORD-INTEGRALS OF STAR BODIES  

Fenghong, Lu (Department of Mathematics, Shanghai University of Electric Power)
Publication Information
Journal of the Korean Mathematical Society / v.47, no.2, 2010 , pp. 277-288 More about this Journal
Abstract
The mixed chord-integrals are defined. The Fenchel-Aleksandrov inequality and a general isoperimetric inequality for the mixed chordintegrals are established. Furthermore, the dual general Bieberbach inequality is presented. As an application of the dual form, a Brunn-Minkowski type inequality for mixed intersection bodies is given.
Keywords
mixed intersection bodies; mixed chord-integrals; Fenchel-Aleksandrov inequality; Bieberbach inequality;
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1 E. Lutwak, Dual mixed volumes, Pacific J. Math. 58 (1975), no. 2, 531–538.   DOI
2 E. Lutwak, A general Bieberbach inequality, Math. Proc. Cambridge Philos. Soc. 78 (1975), no. 3, 493–495.   DOI
3 E. Lutwak, Mixed width-integrals of convex bodies, Israel J. Math. 28 (1977), no. 3, 249–253.   DOI
4 E. Lutwak, Mixed projection inequalities, Trans. Amer. Math. Soc. 287 (1985), no. 1, 91–105.   DOI
5 E. Lutwak, Intersection bodies and dual mixed volumes, Adv. in Math. 71 (1988), no. 2, 232–261.   DOI
6 E. Lutwak, Inequalities for mixed projection bodies, Trans. Amer. Math. Soc. 339 (1993), no. 2, 901–916.   DOI   ScienceOn
7 G. D. Chakerian, Isoperimetric inequalities for the mean width of a convex body, Geometriae Dedicata 1 (1973), no. 3, 356–362.
8 H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press, London, 1934.
9 G. D. Chakerian, The mean volume of boxes and cylinders circumscribed about a convex body, Israel J. Math. 12 (1972), 249–256.   DOI
10 R. J. Gardner, Geometric Tomography, Cambridge Univ. Press, Cambridge, 1995.
11 G. Leng, C. Zhao, B. He, and X. Li, Inequalities for polars of mixed projection bodies, Sci. China Ser. A 47 (2004), no. 2, 175–186.   DOI   ScienceOn
12 E. Lutwak, Width-integrals of convex bodies, Proc. Amer. Math. Soc. 53 (1975), no. 2, 435–439.   DOI
13 L. Santalo, An affine invariant for convex bodies of n-dimensional space, Portugaliae Math. 8 (1949), 155–161.
14 R. Schneider, Convex Body: The Brunn-Minkowski Theory, Cambridge Univ. Press, Cambridge, 1993.
15 G. Zhang, Centered bodies and dual mixed volumes, Trans. Amer. Math. Soc. 345 (1994), no. 2, 777–801.   DOI   ScienceOn
16 C. J. Zhao and G. S. Leng, On polars of mixed projection bodies, J. Math. Anal. Appl. 316 (2006), no. 2, 664–678.   DOI   ScienceOn