Results 11 to 20 of about 4,011 (135)

On Gaussian Brunn-Minkowski inequalities [PDF]

Studia Mathematica, 2008
In this paper, we are interested in Gaussian versions of the classical Brunn-Minkowski inequality. We prove in a streamlined way a semigroup version of the Ehrard inequality for $m$ Borel or convex sets based on a previous work by Borell. Our method also
Barthe, Franck, Huet, Nolwen
core   +8 more sources

On Minkowski's inequality and its application [PDF]

Journal of Inequalities and Applications, 2011
In the paper, we first give an improvement of Minkowski integral inequality. As an application, we get new Brunn-Minkowski-type inequalities for dual mixed volumes.
Cheung Wing-Sum, Zhao Chang-Jian
doaj   +3 more sources

The Functional Orlicz Brunn-Minkowski Inequality for q-Capacity

Journal of Function Spaces, 2020
In this paper, we establish functional forms of the Orlicz Brunn-Minkowski inequality and the Orlicz-Minkowski inequality for the electrostatic q-capacity, which generalize previous results by Zou and Xiong.
Wei Wang, Juan Li, Rigao He, Lijuan Liu
doaj   +2 more sources

On p-radial Blaschke and harmonic Blaschke additions. [PDF]

J Inequal Appl, 2017
In the paper, we first improve the radial Blaschke and harmonic Blaschke additions and introduce the p-radial Blaschke and p-harmonic Blaschke additions.
Zhao CJ.
europepmc   +2 more sources

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, Jin, Hailin, Leng, Gangsong   +2 more
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Quantitative stability for the Brunn–Minkowski inequality [PDF]

Advances in Mathematics, 2017
We prove a quantitative stability result for the Brunn-Minkowski inequality: if $|A|=|B|=1$, $t \in [ ,1- ]$ with $ >0$, and $|tA+(1-t)B|^{1/n}\leq 1+ $ for some small $ $, then, up to a translation, both $A$ and $B$ are quantitatively close (in terms of $ $) to a convex set $K$.
Figalli, Alessio, Jerison, David S.
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The log-Brunn–Minkowski inequality

Advances in Mathematics, 2012
It is conjectured that for origin-symmetric convex bodies, there exist a family of inequalities each of which is stronger than the classical Minkowski mixed-volume inequality and a family of inequalities each of which is stronger than the classical Brunn-Minkowski inequality.
Böröczky, Károly (Ifj.), Lutwak, E., Yang, D., Zhang, G.   +3 more
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The Brunn–Minkowski inequality for volume differences

Advances in Applied Mathematics, 2004
Suppose that \(K\), \(L\), \(D\), \(D'\) are compact domains in \(\mathbb{R}^n\) such that \(D\) and \(D'\) are homothetic and convex and \(D\subset K\), \(D'\subset L\). It is proved (in a more general form) that for the volume \(V\) one has \[ ((V(K+ L)- V(D+ D'))^{1/n}\geq (V(K)- V(D))^{1/n}+ (V(L)- V(D'))^{1/n}.
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The Brunn–Minkowski Inequality, Minkowski's First Inequality, and Their Duals

Journal of Mathematical Analysis and Applications, 2000
Let \(K,L\) be convex bodies in Euclidean space \(\mathbb{E}^n\) with volumes \(V(K)=V(L)=1\), and let \(V_1(K,L)\) denote the mixed volume \(V(K, \dots, K,L)\). Then \[ V(K+L)^{1/n} -2\leq V_1(K,L) -1\leq {1\over n}\bigl(V(K+L)-2^n \bigr). \] These inequalities provide a quantitative improvement of the known equivalence of the Brunn-Minkowski ...
Vassallo, Salvatore Flavio, Gardner, Richard J.   +1 more
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Boundary restricted Brunn–Minkowski inequalities

Communications in Contemporary Mathematics, 2023
In this paper, we explore questions regarding the Minkowski sum of the boundaries of convex sets. Motivated by a question suggested to us by V. Milman regarding the volume of [Formula: see text] where [Formula: see text] and [Formula: see text] are convex bodies, we prove sharp volumetric lower bounds for the Minkowski average of the boundaries of ...
Shiri Artstein-Avidan, Tomer Falah, Boaz A. Slomka   +2 more
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