Affine Isoperimetric Inequalities for L p Geominimal Surface Area

2014 ◽  
pp. 167-176 ◽  
Author(s):  
Baocheng Zhu ◽  
Jiazu Zhou ◽  
Wenxue Xu
Keyword(s):  
Surface Area ◽  
Isoperimetric Inequalities ◽  
Geominimal Surface Area

scholarly journals ISOPERIMETRIC INEQUALITIES FOR Lp GEOMINIMAL SURFACE AREA

2011 ◽  
Vol 53 (3) ◽  
pp. 717-726 ◽  
Author(s):  
BAOCHENG ZHU ◽  
NI LI ◽  
JIAZU ZHOU
Keyword(s):  
Convex Body ◽  
Surface Area ◽  
Type Inequality ◽  
Isoperimetric Inequalities ◽  
Surface Areas ◽  
Cyclic Inequality ◽  
Geominimal Surface Area

AbstractIn this paper, we establish a number of Lp-affine isoperimetric inequalities for Lp-geominimal surface area. In particular, we obtain a Blaschke–Santaló type inequality and a cyclic inequality between different Lp-geominimal surface areas of a convex body.

scholarly journals DualLp-Mixed Geominimal Surface Area and Related Inequalities

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Tongyi Ma ◽  
Yibin Feng
Keyword(s):  
Surface Area ◽  
Integral Formula ◽  
Isoperimetric Inequalities ◽  
Surface Areas ◽  
Geominimal Surface Area

The integral formula of dualLp-geominimal surface area is given and the concept of dualLp-geominimal surface area is extended to dualLp-mixed geominimal surface area. Properties for the dualLp-mixed geominimal surface areas are established. Some inequalities, such as analogues of Alexandrov-Fenchel inequalities, Blaschke-Santaló inequalities, and affine isoperimetric inequalities for dualLp-mixed geominimal surface areas, are also obtained.

scholarly journals The General Dual Orlicz Geominimal Surface Area

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Ni Li ◽  
Shuang Mou
Keyword(s):  
Surface Area ◽  
Mixed Volume ◽  
Subject Classification ◽  
Dual Orlicz Mixed Volume ◽  
Geominimal Surface Area ◽  
Orlicz Mixed Volume

In this paper, we study the general dual Orlicz geominimal surface area by the general dual Orlicz mixed volume which was introduced by Gardner et al. (2019). We find the conditions to the existence of the general dual Orlicz-Petty body and hence prove the continuity of the general geominimal surface area in the Orlicz setting (2010 Mathematics Subject Classification: 52A20, 53A15).

scholarly journals Lp mixed geominimal surface area

2015 ◽  
Vol 422 (2) ◽  
pp. 1247-1263 ◽  
Author(s):  
Baocheng Zhu ◽  
Jiazu Zhou ◽  
Wenxue Xu
Keyword(s):  
Surface Area ◽  
Geominimal Surface Area
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