On the L p -dual mixed volumes

2013 ◽  
Vol 29 (9) ◽  
pp. 1647-1654
Author(s):  
Lian Ying Chen ◽  
Chang Jian Zhao
Keyword(s):  
Mixed Volumes ◽  
Dual Mixed Volumes

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 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

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

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

scholarly journals Lp-DUAL MIXED GEOMINIMAL SURFACE AREA

2013 ◽  
Vol 56 (1) ◽  
pp. 229-239 ◽  
Author(s):  
YIBIN FENG ◽  
WEIDONG WANG
Keyword(s):  
Surface Area ◽  
Mixed Volumes ◽  
Geominimal Surface Area ◽  
Dual Mixed Volumes

AbstractLutwak (Adv. Math., vol. 118(2), 1996, pp. 244–294) defined the notion of Lp-geominimal surface area based on Lp-mixed volumes. Recently, Wang and Qi (J. Inequal. Appl., vol. 2011, 2011, pp. 1–10) introduced the concept of Lp-dual geominimal surface area based on Lp-dual mixed volumes. In this paper, based on Lp-dual mixed quermassintegrals, we define the concept of Lp-dual mixed geominimal surface area and establish several inequalities for this new notion.

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