收稿日期: 2015-05-11
网络出版日期: 2016-12-30
A new proof of the Brunn-Minkowski inequality
Received date: 2015-05-11
Online published: 2016-12-30
证明了Knöthe映射的基本性质, 计算了几个特殊凸体间的Knöthe映射. 作为应用,利用Knöthe映射给出了Brunn-Minkowski不等式的一个新证明.
关键词： Brunn-Minkowski不等式; Knöthe映射; 凸体
廖婷 . Brunn-Minkowski不等式的一个新证明[J]. 上海大学学报(自然科学版), 2016 , 22(6) : 763 -774 . DOI: 10.3969/j.issn.1007-2861.2015.03.001
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
[1] Steiner J. Einfache beweise der isoperimetrischen hauptsätze [J]. J Reine Angew Math, 1838, 18: 281-296.
[2] Haberl C, Schuster F. General Lp 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. Lp 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.
/
| 〈 |
|
〉 |
