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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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The dimensional Brunn–Minkowski inequality in Gauss space
Journal of Functional Analysis, 2021 Let $γ_n$ be the standard Gaussian measure on $\mathbb{R}^n$. We prove that for every symmetric convex sets $K,L$ in $\mathbb{R}^n$ and every $λ\in(0,1)$, $$γ_n(λK+(1-λ)L)^{\frac{1}{n}} \geq λγ_n(K)^{\frac{1}{n}}+(1-λ)γ_n(L)^{\frac{1}{n}},$$ thus settling a problem raised by Gardner and Zvavitch (2010).
Eskenazis, Alexandros +1 more
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Orlicz Mean Dual Affine Quermassintegrals
Journal of Function Spaces, 2018 Our main aim is to generalize the mean dual affine quermassintegrals to the Orlicz space. Under the framework of dual Orlicz-Brunn-Minkowski theory, we introduce a new affine geometric quantity by calculating the first Orlicz variation of the mean dual ...
Chang-Jian Zhao, Wing-Sum Cheung
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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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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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On Discrete LOG-Brunn--Minkowski Type Inequalities
SIAM Journal on Discrete Mathematics, 2022 The conjectured log-Brunn--Minkowski inequality says that the volume of centrally symmetric convex bodies $K,L\subset\mathbb{R}^n$ satisfies ${vol}\bigl((1-\lambda)\cdot K+_0\lambda\cdot L\bigr) \geq{vol}(K)^{1-\lambda}{vol}(L)^\lambda$, $\lambda\in(0,1)$, and is known to be true in the plane and for particular classes of symmetric convex bodies in ...
Hernández Cifre, María de los Ángeles +1 more
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A Curved Brunn Minkowski Inequality for the Symmetric Group [PDF]
The Electronic Journal of Combinatorics, 2016 In this paper, we construct an injection $A \times B \rightarrow M \times M$ from the product of any two nonempty subsets of the symmetric group into the square of their midpoint set, where the metric is that corresponding to the conjugacy class of transpositions. If $A$ and $B$ are disjoint, our construction allows to inject two copies of $A \times B$
Neeranartvong, Weerachai +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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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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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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