SOME INEQUALITIES ABOUT DUAL MIXED VOLUMES OF STAR BODIES

2005 ◽  
Vol 25 (3) ◽  
pp. 505-510 ◽  
Author(s):  
Xiaoyan Li ◽  
Gangsong Leng
Keyword(s):  
Mixed Volumes ◽  
Dual Mixed Volumes ◽  
Star Bodies

scholarly journals Dual mixed volumes and the slicing problem

2006 ◽  
Vol 207 (2) ◽  
pp. 566-598 ◽  
Author(s):  
Emanuel Milman
Keyword(s):  
Mixed Volumes ◽  
Dual Mixed Volumes

scholarly journals Star Valuations and Dual Mixed Volumes

1996 ◽  
Vol 121 (1) ◽  
pp. 80-101 ◽  
Author(s):  
Daniel A. Klain
Keyword(s):  
Mixed Volumes ◽  
Dual Mixed Volumes

Orlicz dual affine quermassintegrals

2018 ◽  
Vol 30 (4) ◽  
pp. 929-945 ◽  
Author(s):  
Chang-Jian Zhao
Keyword(s):  
Orlicz Space ◽  
Minkowski Inequality ◽  
Mixed Volumes ◽  
Geometric Quantity ◽  
First Order ◽  
Order Variation ◽  
Dual Affine ◽  
Dual Minkowski Inequality ◽  
Dual Mixed Volumes ◽  
Special Case

Abstract In the paper, our main aim is to generalize the dual affine quermassintegrals to the Orlicz space. Under the framework of Orlicz dual Brunn–Minkowski theory, we introduce a new affine geometric quantity by calculating the first-order variation of the dual affine quermassintegrals, and call it the Orlicz dual affine quermassintegral. The fundamental notions and conclusions of the dual affine quermassintegrals and the Minkoswki and Brunn–Minkowski inequalities for them are extended to an Orlicz setting, and the related concepts and inequalities of Orlicz dual mixed volumes are also included in our conclusions. The new Orlicz–Minkowski and Orlicz–Brunn–Minkowski inequalities in a special case yield the Orlicz dual Minkowski inequality and Orlicz dual Brunn–Minkowski inequality, which also imply the {L_{p}} -dual Minkowski inequality and Brunn–Minkowski inequality for the dual affine quermassintegrals.

scholarly journals The Dual Orlicz–Aleksandrov–Fenchel Inequality

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2005
Author(s):  
Chang-Jian Zhao
Keyword(s):  
Orlicz Space ◽  
Minkowski Inequality ◽  
Mixed Volume ◽  
Mixed Volumes ◽  
Geometric Quantity ◽  
First Order ◽  
Special Cases ◽  
Star Bodies

In this paper, the classical dual mixed volume of star bodies V˜(K1,⋯,Kn) and dual Aleksandrov–Fenchel inequality are extended to the Orlicz space. Under the framework of dual Orlicz-Brunn-Minkowski theory, we put forward a new affine geometric quantity by calculating first order Orlicz variation of the dual mixed volume, and call it Orlicz multiple dual mixed volume. We generalize the fundamental notions and conclusions of the dual mixed volume and dual Aleksandrov-Fenchel inequality to an Orlicz setting. The classical dual Aleksandrov-Fenchel inequality and dual Orlicz-Minkowski inequality are all special cases of the new dual Orlicz-Aleksandrov-Fenchel inequality. The related concepts of Lp-dual multiple mixed volumes and Lp-dual Aleksandrov-Fenchel inequality are first derived here. As an application, the dual Orlicz–Brunn–Minkowski inequality for the Orlicz harmonic addition is also established.

scholarly journals Characterization of dual mixed volumes via polymeasures

2015 ◽  
Vol 426 (2) ◽  
pp. 688-699 ◽  
Author(s):  
Carlos H. Jiménez ◽  
Ignacio Villanueva
Keyword(s):  
Mixed Volumes ◽  
Dual Mixed Volumes

scholarly journals Dual mixed volumes

1975 ◽  
Vol 58 (2) ◽  
pp. 531-538 ◽  
Author(s):  
Erwin Lutwak
Keyword(s):  
Mixed Volumes ◽  
Dual Mixed Volumes

scholarly journals From John to Gauss–John positions via dual mixed volumes

2007 ◽  
Vol 328 (1) ◽  
pp. 550-566 ◽  
Author(s):  
Jesús Bastero ◽  
Julio Bernués ◽  
Miguel Romance
Keyword(s):  
Mixed Volumes ◽  
Dual Mixed Volumes
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