Results 151 to 160 of about 2,936 (172)

Remarks on the conjectured log-Brunn–Minkowski inequality

, 2013
Böröczky, Lutwak, Yang and Zhang recently conjectured a certain strengthening of the Brunn-Minkowski inequality for symmetric convex bodies, the so-called log-Brunn-Minkowski inequality.
Christos Saroglou
semanticscholar   +1 more source

On a Discrete Brunn--Minkowski Type Inequality

SIAM Journal on Discrete Mathematics, 2018
The classical Brunn-Minkowski inequality for the Minkowski sum of two compact sets \(K\) and \(L\) in \(\mathbb R^n\) states that \[ \mathrm{vol}(K+L)^{1/n} \geq\mathrm{vol}(K)^{1/n} + \mathrm{vol}(L)^{1/n}. \] On the other hand, if \(A\) and \(B\) are finite subsets of \(\mathbb R^n\) and \(|\;|\) stands for their cardinality, a direct discrete ...
Hernández Cifre, María A., Iglesias, David, Nicolás, Jesús Yepes   +2 more
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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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On Brunn–Minkowski-Type Inequalities for Polar Bodies

The Journal of Geometric Analysis, 2014
Let \( {\mathcal K}^{n}_0\) be the set of all convex bodies in \( {\mathbb R}^n \) containing the origin as an interior point. Given \( K, L \in {\mathcal K}^{n}_0 \), \( 1 \leq p \leq \infty \), and \( \lambda, \mu \geq 0 \), we denote by \( \lambda \cdot K +_p \, \mu \cdot L \) their Firey linear combination, its support function is defined by \[ h (\
Hernández Cifre, María A., Yepes Nicolás, Jesús   +1 more
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Notes on the log-Brunn-Minkowski inequality

Acta Mathematica Scientia, 2023
Yunlong Yang, Nan Jiang, Deyan Zhang
semanticscholar   +1 more source

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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The L-Brunn-Minkowski inequality for p < 1

, 2020
Shibing Chen, Yong Huang, Qi-rui Li, Jiakun Liu   +3 more
semanticscholar   +1 more source

The $${\varphi}$$ φ -Brunn–Minkowski inequality

Acta Mathematica Hungarica, 2018
For strictly increasing concave functions $${\varphi}$$ whose inverse functions are log-concave, the $${\varphi}$$
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The Brunn-Minkowski inequality in Gauss space

, 1975
C. Borell
semanticscholar   +1 more source