Brunn-Minkowski不等式的一个新证明

doi:10.3969/j.issn.1007-2861.2015.03.001

Journal of Shanghai University（Natural Science Edition） ›› 2016, Vol. 22 ›› Issue (6): 763-774.doi: 10.3969/j.issn.1007-2861.2015.03.001

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A new proof of the Brunn-Minkowski inequality

LIAO Ting

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2015-05-11 Online:2016-12-30 Published:2016-12-30

Several important properties of Knöthe map were obtained, and then the Knöthe maps between certain specific convex bodies were calculated. As an application, a new proof of Brunn-Minkowski inequality using Knöthe map was given.

Key words: Brunn-Minkowski inequality, Knöthe map , convex body

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LIAO Ting. A new proof of the Brunn-Minkowski inequality[J]. Journal of Shanghai University（Natural Science Edition）, 2016, 22(6): 763-774.

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References

[1] Steiner J. Einfache beweise der isoperimetrischen hauptsätze [J]. J Reine Angew Math, 1838, 18: 281-296.
[2] Haberl C, Schuster F. General L_p affine isoperimetric inequalities [J]. J Differential Geom, 2009, 83: 1-26.
[3] Klartag B, Milman V. Isomorphic Steiner symmetrization [J]. Invent Math, 2003, 153: 463-485.

[4] Lutwak E, Yang D, Zhang G. L_p affine isoperimetric inequalities [J]. J Differential Geom, 2000, 56: 111-132.
[5] Lutwak E, Yang D, Zhang G. Orlicz projection bodies [J]. Adv Math, 2010, 223: 220-242.
[6] Lutwak E, Yang D, Zhang G. Orlicz centroid bodies [J]. J Differential Geom, 2010, 84: 365-387.
[7] Schuster F, Weberndorger M. Volume inequalities for asymmetric Wulff shapes [J]. J Differential Geom, 2012, 92: 263-283.
[8] Knöthe H. Contributions to the theory of convex bodies [J]. Mich Math J, 1957, 4: 39-52.
[9] Gardner R. Geometric tomography [M]. New York: Cambridge University Press, 1995.
[10] Schneider R. Convex bodies: the Brunn-Minkowski theory [M]. Cambridge: Cambridge University
Press, 2014.

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