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Journal of Inequalities and Applications
Published in: Journal of Inequalities and Applications 1/2006

Open Access 01-12-2006 | Research Article

Dual https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F84825/MediaObjects/13660_2005_Article_1648_IEq1_HTML.gif affine isoperimetric inequalities

Authors: Si Lin, Xiong Bin, Yu Wuyang

Published in: Journal of Inequalities and Applications | Issue 1/2006

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Abstract

We establish some inequalities for the dual https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F84825/MediaObjects/13660_2005_Article_1648_IEq2_HTML.gif -centroid bodies which are the dual forms of the results by Lutwak, Yang, and Zhang. Further, we establish a Brunn-Minkowski-type inequality for the polar of dual https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F84825/MediaObjects/13660_2005_Article_1648_IEq3_HTML.gif -centroid bodies.
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Literature
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Gardner RJ: Geometric Tomography, Encyclopedia of Mathematics and Its Applications. Volume 58. Cambridge University Press, Cambridge; 1995:xvi+424.
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Lutwak E: The Brunn-Minkowski-Firey theory. I. Mixed volumes and the Minkowski problem. Journal of Differential Geometry 1993,38(1):131–150.MATHMathSciNet
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Lutwak E, Yang D, Zhang G: affine isoperimetric inequalities. Journal of Differential Geometry 2000,56(1):111–132.MATHMathSciNet
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Lutwak E, Yang D, Zhang G: A new ellipsoid associated with convex bodies. Duke Mathematical Journal 2000,104(3):375–390. 10.1215/S0012-7094-00-10432-2MATHMathSciNetCrossRef
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Lutwak E, Yang D, Zhang G: John ellipsoids. Proceedings of the London Mathematical Society. Third Series 2005,90(2):497–520. 10.1112/S0024611504014996MATHMathSciNetCrossRef
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Lutwak E, Zhang G: Blaschke-Santaló inequalities. Journal of Differential Geometry 1997,47(1):1–16.MATHMathSciNet
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Schneider R: Convex Bodies: The Brunn-Minkowski Theory, Encyclopedia of Mathematics and Its Applications. Volume 44. Cambridge University Press, Cambridge; 1993:xiv+490.
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Thompson AC: Minkowski Geometry, Encyclopedia of Mathematics and Its Applications. Volume 63. Cambridge University Press, Cambridge; 1996:xvi+346.
Metadata
Title
Dual affine isoperimetric inequalities
Authors
Si Lin
Xiong Bin
Yu Wuyang
Publication date
01-12-2006
Publisher
Springer International Publishing
Published in
Journal of Inequalities and Applications / Issue 1/2006
Electronic ISSN: 1029-242X
DOI
https://doi.org/10.1155/JIA/2006/84825

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