Results 121 to 130 of about 543,197 (136)

The Brunn–Minkowski Inequality and Nonconvex Sets

Geometriae Dedicata, 1997
The author aims at improving the Brunn-Minkowski inequality for nonconvex sets, by introducing the convex hull of one of the sets into the estimate. For a Borel set \(B\) in \(\mathbb{R}^d\), define \[ \xi(a): =\inf\bigl\{\mu (A+B):A \text{ Borel set, } \mu(A)=a \bigr\}, \] where \(\mu\) denotes Lebesgue measure, and let \(\mu(B)=b\), \(\mu(\text{conv}
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On the similarity of the entropy power inequality and the Brunn- Minkowski inequality (Corresp.)

IEEE Transactions on Information Theory, 1984
Summary: The entropy power inequality states that the effective variance (entropy power) of the sum of two independent random variables is greater than the sum of their effective variances. The Brunn-Minkowski inequality states that the effective radius of the set sum of two sets is greater than the sum of their effective radii. Both these inequalities
Max H. M. Costa, Thomas M. Cover
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Brunn-Minkowski inequality for multiplicities

Inventiones Mathematicae, 1996
Let a connected reductive group \(G\) act in a vector space \(V\). Suppose \(X\) is a closed \(G\)-stable irreducible subvariety of \(\mathbb P(V)\). Let \(F[X] =\bigoplus_mF[X]_m\) be the homogeneous coordinate ring of \(X\). Consider the decomposition of \(F[X]_m\) as \(G\)-module \(F[X]_m =\bigoplus_{\lambda}\mu_m(\lambda)V^\lambda\), where \(V ...
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Dual Brunn–Minkowski inequality for volume differences

Geometriae Dedicata, 2009
The author proves several dual Brunn-Minkowski type inequalities for the volume difference, dual quermassintegral difference, width-integral difference or dual mixed volume difference of star bodies. For instance, it is shown that if \(K,L,M,M'\) are star bodies in \({\mathbb R}^n\) such that \(M'\) is a dilation of \(M\) and \(K\subset M\), \(L\subset
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The Orlicz Brunn–Minkowski Inequality for the Projection Body

Journal of Geometric Analysis, 2020
Ge Xiong, Du Zou
exaly  

$$L_p$$-Brunn–Minkowski inequality for projection bodies

Acta Mathematica Hungarica
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Log-Brunn-Minkowski Inequality in ℝ³

Proceedings of the American Mathematical Society, 2019
Yunlong Yang, Deyan Zhang
exaly  

The Dual Log-Brunn-Minkowski Inequalities

Taiwanese Journal of Mathematics, 2016
Lijuan Liu
exaly  

Brunn-Minkowski Inequality and Its Aftermath

Journal of Multivariate Analysis, 1980
Somesh Das Gupta
exaly  

Dual Mixed Orlicz–Brunn–Minkowski Inequality and Dual Orlicz Mixed Quermassintegrals

Indagationes Mathematicae, 2017
Weidong Wang
exaly