q-dual mixed volumes and L p -intersection bodies

2019 ◽  
Vol 26 (1) ◽  
pp. 149-157
Author(s):  
Chang-Jian Zhao ◽  
Wing-Sum Cheung
Keyword(s):  
Mixed Volumes ◽  
Intersection Bodies ◽  
Mixed Intersection Bodies ◽  
Dual Mixed Volumes

Abstract In this paper, we introduce the new notions of {L_{p}} -intersection and mixed intersection bodies. Inequalities for the q-dual volume sum of {L_{p}} -mixed intersection bodies are established.

scholarly journals $p$-Minkowski inequalities for mixed intersection bodies

2010 ◽  
Vol 11 (2) ◽  
pp. 121
Author(s):  
Zhao Chang-jian ◽  
Mihály Bencze
Keyword(s):  
Intersection Bodies ◽  
Mixed Intersection 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.

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