Results 21 to 30 of about 813 (131)
INEQUALITIES BETWEEN MIXED VOLUMES OF CONVEX BODIES: VOLUME BOUNDS FOR THE MINKOWSKI SUM
Mathematika, Volume 66, Issue 4, Page 1003-1027, October 2020., 2020 Abstract In the course of classifying generic sparse polynomial systems which are solvable in radicals, Esterov recently showed that the volume of the Minkowski sum P1+⋯+Pd of d‐dimensional lattice polytopes is bounded from above by a function of order O(m2d), where m is the mixed volume of the tuple (P1,⋯,Pd).
Gennadiy Averkov +2 more
wiley +1 more source
Isoperimetric and Brunn-Minkowski inequalities for the (p, q)-mixed geominimal surface areas
Open Mathematics, 2022 Motivated by the celebrated work of Lutwak, Yang and Zhang [1] on (p,q)\left(p,q)-mixed volumes and that of Feng and He [2] on (p,q)\left(p,q)-mixed geominimal surface areas, we in the present paper establish and confirm the affine isoperimetric and ...
Zhang Juan, Wang Weidong, Zhao Peibiao
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The General Dual Orlicz Geominimal Surface Area
Journal of Function Spaces, Volume 2020, Issue 1, 2020., 2020 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
Ni Li, Shuang Mou, Alberto Fiorenza
wiley +1 more source
Uniqueness of Solutions to a Nonlinear Elliptic Hessian Equation
Journal of Applied Mathematics, 2016 Through an Alexandrov-Fenchel inequality, we establish the general Brunn-Minkowski inequality. Then we obtain the uniqueness of solutions to a nonlinear elliptic Hessian equation on Sn.
Siyuan Li
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Functional Geominimal Surface Area and Its Related Affine Isoperimetric Inequality
Journal of Function Spaces, Volume 2020, Issue 1, 2020., 2020 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.
Niufa Fang, Jin Yang, Chang-Jian Zhao
wiley +1 more source
Some new Brunn-Minkowski-type inequalities in convex bodies
International Journal of Mathematics and Mathematical Sciences, 2005 We establish some analogues of the Brunn-Minkowski inequalities on convex bodies and the Minkowski inequality and their inverse versions. As an application, we generalize and improve some interrelated results.
Zhao Chang-Jian +2 more
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On the Discrete Orlicz Electrostatic q‐Capacitary Minkowski Problem
Journal of Function Spaces, Volume 2020, Issue 1, 2020., 2020 We establish the existence of solutions to the Orlicz electrostatic q‐capacitary Minkowski problem for polytopes. This contains a new result of the discrete Lp electrostatic q‐capacitary Minkowski problem for p < 0and 1 < q < n.
Yibin Feng, Yanping Zhou, Youjiang Lin
wiley +1 more source
Dual Orlicz geominimal surface area
Journal of Inequalities and Applications, 2016 The L p $L_{p}$ -geominimal surface area was introduced by Lutwak in 1996, which extended the important concept of the geominimal surface area. Recently, Wang and Qi defined the p-dual geominimal surface area, which belongs to the dual Brunn-Minkowski ...
Tongyi Ma, Weidong Wang
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The Brunn–Minkowski inequality for volume differences
, 2004 In this paper, we establish some theorems for the volume differences of compact domains, which are extensions of the Brunn–Minkowski inequality, Minkowski inequality, and isoperimetric inequality.
Leng, Gangsong
core +1 more source
General L p $L_{p}$ -mixed chord integrals of star bodies
Journal of Inequalities and Applications, 2016 The notion of general mixed chord integrals of star bodies was introduced by Feng and Wang. In this paper, we extend the concept of the general mixed chord integrals to general L p $L_{p}$ -mixed chord integrals of star bodies.
Zhaofeng Li, Weidong Wang
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