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 Functional Geominimal Surface Area and Its Related Affine Isoperimetric Inequality

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Niufa Fang ◽  
Jin Yang
Keyword(s):  
Surface Area ◽  
Isoperimetric Inequality ◽  
Convex Bodies ◽  
Mixed Volume ◽  
Concave Functions ◽  
Variation Formula ◽  
First Variation ◽  
The First Variation ◽  
Geominimal Surface Area ◽  
Affine Isoperimetric Inequality

The first variation of the total mass of log-concave functions was studied by Colesanti and Fragalà, which includes the Lp mixed volume of convex bodies. Using Colesanti and Fragalà’s first variation formula, we define the geominimal surface area for log-concave functions, and its related affine isoperimetric inequality is also established.

scholarly journals Some inequalities for the (p,q)-mixed geominimal surface areas and Lp radial Blaschke-Minkowski homomorphisms

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1393-1403
Author(s):  
Juan Zhang ◽  
Weidong Wang
Keyword(s):  
Surface Area ◽  
Mixed Volume ◽  
Surface Areas ◽  
Cyclic Inequality ◽  
Geominimal Surface Area

Wang et al. introduced Lp radial Blaschke-Minkowski homomorphisms based on Schuster?s radial Blaschke-Minkowski homomorphisms. In 2018, Feng and He gave the concept of (p,q)-mixed geominimal surface area according to the Lutwak, Yang and Zhang?s (p,q)-mixed volume. In this article, associated with the (p,q)-mixed geominimal surface areas and the Lp radial Blaschke-Minkowski homomorphisms, we establish some inequalities including two Brunn-Minkowski type inequalities, a cyclic inequality and two monotonic inequalities.

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.

Asymptotic Formulae for the Lattice Point Enumerator

1999 ◽  
Vol 51 (2) ◽  
pp. 225-249 ◽  
Author(s):  
U. Betke ◽  
K. Böröczky
Keyword(s):  
Convex Body ◽  
Surface Area ◽  
Positive Curvature ◽  
Convex Bodies ◽  
Mixed Volume ◽  
Lattice Points ◽  
Asymptotic Formulae ◽  
General Convex ◽  
Lattice Surface ◽  
Small Deformations

AbstractLet M be a convex body such that the boundary has positive curvature. Then by a well developed theory dating back to Landau and Hlawka for large λ the number of lattice points in λM is given by G(λM) = V(λM) + O(λd−1−ε(d)) for some positive ε(d). Here we give for general convex bodies the weaker estimatewhere SZd (M) denotes the lattice surface area of M. The term SZd is optimal for all convex bodies and o(λd−1) cannot be improved in general. We prove that the same estimate even holds if we allow small deformations of M.Further we deal with families {Pλ} of convex bodies where the only condition is that the inradius tends to infinity. Here we havewhere the convex body K satisfies some simple condition, V(Pλ; K; 1) is some mixed volume and S(Pλ) is the surface area of Pλ.

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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