Results 21 to 30 of about 3,973 (97)
Some inequalities for star duality of the radial Blaschke-Minkowski homomorphisms
Open Mathematics, 2020 In 2006, Schuster introduced the radial Blaschke-Minkowski homomorphisms. In this article, associating with the star duality of star bodies and dual quermassintegrals, we establish Brunn-Minkowski inequalities and monotonic inequality for the radial ...
Zhao Xia, Wang Weidong, Lin Youjiang
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Orlicz-Aleksandrov-Fenchel Inequality for Orlicz Multiple Mixed Volumes
Journal of Function Spaces, 2018 Our main aim is to generalize the classical mixed volume V(K1,…,Kn) and Aleksandrov-Fenchel inequality to the Orlicz space. In the framework of Orlicz-Brunn-Minkowski theory, we introduce a new affine geometric quantity by calculating the Orlicz first ...
Chang-Jian Zhao
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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
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The openness conjecture and complex Brunn-Minkowski inequalities [PDF]
, 2014 We discuss recent versions of the Brunn-Minkowski inequality in the complex setting, and use it to prove the openness conjecture of Demailly and Koll\'ar.Comment: This is an account of the results in arXiv:1305.5781 together with some background ...
B. Berndtsson +13 more
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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
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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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An equivalence form of the Brunn-Minkowski inequality for volume differences [PDF]
, 2007 In this paper, we establish an equivalence form of the Brunn-Minkowski inequality for volume differences. As an application, we obtain a general and strengthened form of the dual Kneser-Süss inequality.
Cheung, WS, Zhao, CJ
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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
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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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