Results 41 to 50 of about 2,936 (172)
The Orlicz Brunn–Minkowski inequality
Advances in Mathematics, 2014 The Orlicz-Brunn-Minkowski theory was introduced by Lutwak, Yang and Zhang, being an extension of the classical Brunn-Minkowski theory. It represents a generalization of the \(L_p\)-Brunn-Minkowski theory. For a convex, strictly increasing \(\phi:[0,\infty]\longrightarrow [0,\infty)\), with \(\phi(0)=0\) and \(K,L\) convex and compact sets containing ...
Xi, Dongmeng +2 more
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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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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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Sharp $L^1$ Inequalities for Sup-Convolution
Discrete Analysis, 2023 Sharp $L^1$ Inequalities for Sup-Convolution, Discrete Analysis 2023:7, 16 pp. Let $f$ and $g$ be two real-valued functions defined on a compact convex subset $C$ of $\mathbb R^k$.
Hunter Spink +2 more
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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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The Brunn-Minkowski inequality [PDF]
Bulletin of the American Mathematical Society, 2002 This is a basic and high quality survey on the subject related to the isoperimetric inequality. As the author writes: ``This guide explains the relationship between Brunn-Minkowski inequality (B-M-I) and other inequalities in geometry and analysis, and some applications.'' This work can be considered as the up-to-date version of the excellent survey ...
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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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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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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 Brunn-Minkowski inequalities induced by polarity
Advances in Mathematics, 2020 We prove a new family of inequalities, which compare the integral of a geometric convolution of non-negative functions with the integrals of the original functions. For classical inf-convolution, this type of inequality is called the Pr kopa-Leindler inequality, which, restricted to indicators of convex bodies, gives the classical Brunn-Minkowski ...
Artstein-Avidan, S. +2 more
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