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武汉大学学报 英文版 | Wuhan University Journal of Natural Sciences
Wan Fang
CNKI
CSCD
Wuhan University
Latest Article
The Reverse Petty Projection Inequality
Time:2019-8-28  
LIN Youjiang
School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
Abstract:
It is proved that if K is an origin-symmetric convex body in R2 and Π*K is the polar projection body of K, then the volumes of K and Π*K satisfy the inequality V(K)V(Π*K) ⩾ 2 with equality if K is a parallelogram.
Key words:convex body; polar body; projection body; the reverse Petty projection inequality
CLC number:O 178; O 18
References:
[1]	Bolker E D. A class of convex bodies [J]. Trans Amer Math Soc, 1969, 145: 323-345.
[2]	Bourgain J, Lindenstrauss J. Projection Bodies, Geometric Aspects of Functional Analysis Springer Lecture Notes in Math[M]. New York: Springer-Verlag, 1988. 
[3]	Gardner R J. Geometric Tomography [M]. Cambridge: Cam-bridge University Press, 2006.
[4]	Goodey P R, Weil W. Zonoids and Generalizations, Hand-book of Convex Geometry [M]. Amsterdam: North- Holland, 1993.
[5]	Leichtwei B H. Affine Geometry of Convex Bodies [M].  Heidelberg: Springer-Verlag, 1998.
[6]	Petty C M. Projection bodies [J]. Kbenhavns Univ Mat Inst, 1967, 1: 234-241.
[7]	Schneider R. Convex Bodies: The Brunn-Minkowski Theory [M]. Second Ed. Cambridge: Cambridge University Press, 2014.
[8]	Schneider R, Weil W. Zonoids and Related Topics, Convexity and Its Applications [M]. Basel: Birkhauser, 1983.
[9]	Ball K. Volume ratios and a reverse isoperimetric inequality [J]. J London Math Soc, 1991, 44: 351-359.
[10]	Zhang G Y. Restricted chord projection and affine inequalities [J]. Geom Dedicata, 1991, 39: 213-222.
[11]	Gardner R J, Zhang G Y. Affine inequalities and radial mean bodies [J]. Amer J Math, 1998, 120: 505- 528.
[12]	Du C M, Guo L J, Leng G S. Volume inequalities for Orlicz mean bodies [J]. Proc Indian Acad Sci Math Sci, 2015, 125: 57-70.
[13]	Du C M, Leng G S, Xi D M. Volume inequalities for Orlicz mean zonoids [J]. Math Inequal App, 2014, 17: 1529-1541.
[14]	Wang W D. On extensions of the Zhang’s projection ine-quality [J]. Adv Appl Math Sci, 2010, 2: 199-207.
[15]	Wang W D, Zhang T. Inequalities for dual quermassintegrals of the redial pth mean bodies [J]. J Inequal Appl, 2014, 1: 252-262.
[16]	Zhou Y P, He B W. On LYZ’s conjecture for the U-functional [J]. Adv in Appl Math, 2017, 87: 43-57.
[17]	Lin Y J, Leng G S. Convex bodies with minimal volume product in  —A new proof [J]. Discrete Math, 2010, 310: 3018-3025.
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