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Firey linear combinations of convex bodies. (English) Zbl 1212.52007

Summary: For convex bodies, the Firey linear combinations were introduced and studied in several papers. In this paper, the mean width of the Firey linear combinations of convex bodies is studied, and the lower bound of the mean width of the Firey linear combinations of a convex body and its polar body are given.

MSC:

52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
52A40 Inequalities and extremum problems involving convexity in convex geometry
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[1] Firey W J. p-means of convex bodies [J]. Mathematica Scandinavica, 1962, 10: 17–24. · Zbl 0188.27303
[2] Firey W J. Some applications of means of convex bodies [J]. Pacific Journal of Mathematics, 1964, 14(1): 53–60. · Zbl 0126.38405
[3] Lutwak E. The Brunn-Minkowski-Firey theory I: mixed volumes and the Minkowski problem [J]. Journal of Differential Geometry, 1993, 38(1): 131–150. · Zbl 0788.52007
[4] Lutwak E. The Brunn-Minkowski-Firey theory II: afine and geominimal surface areas [J]. Advances in Mathematics, 1996, 118(2): 244–294. · Zbl 0853.52005
[5] Firey W J. Polar means of convex bodies and a dual to the Brunn-Minkowski theorem [J]. Canadian Journal of Mathematics, 1961, 13: 444–453. · Zbl 0126.18005
[6] Chai Y D, Lee, Y S. Harmonic radial combinations and dual mixed volumes [J]. Asian Journal of Mathematics, 2001, 5(3): 493–498. · Zbl 1009.52015
[7] Alexandrov A D. On the theory of mixed volumes of convex bodies [J]. Matematicheskii Sbornik, 1938, 45(3): 28–46.
[8] Burago Y D, Zalgaller V A. Geometric inequalities [M]. Berlin: Springer-Verlag, 1988. · Zbl 0633.53002
[9] Gardner R. Geometric tomography [M]. Cambridge, Eng: Cambridge University Press, 1995.
[10] Delin Ren. Topics in integral geometry [M]. Sigapore: World Scientific, 1988. · Zbl 0658.53066
[11] Schneider R. Convex bodies: the Brunn-Minkowski theory [M]. Cambridge, Eng: Cambridge University Press, 1993. · Zbl 0798.52001
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