Results 111 to 120 of about 4,011 (135)

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

Acta Mathematica Hungarica, 2018
For strictly increasing concave functions $${\varphi}$$ whose inverse functions are log-concave, the $${\varphi}$$
Songjun Lv
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The Dual $$\phi $$-Brunn–Minkowski Inequality

Mediterranean Journal of Mathematics, 2021
Let \(K, L\subset\mathbb{R}^n\) be star bodies (i.e., star-shaped sets with respect to the origin, having continuous radial function), and let \(\rho_K\) and \(\rho_L\) be the radial functions of \(K\) and \(L\), respectively. Let \(\phi\in C^1((0,\infty))\) be strictly decreasing and concave, and assume that \(\log\circ\phi^{-1}\) is a convex function.
Shi, Wei, Li, Tian, Wang, Weidong
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On Discrete LOG-Brunn--Minkowski Type Inequalities

SIAM Journal on Discrete Mathematics, 2022
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Hernández Cifre, María A., Lucas, Eduardo   +1 more
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Brunn-Minkowski inequality

2000
This section is basic for our further considerations and is devoted to those convex sets which lie in finite-dimensional topological vector spaces. As mentioned in the previous section, if E is an arbitrary finite-dimensional (Hausdorff) topological vector space, then E is isomorphic to some Euclidean space R n .
V. V. Buldygin, A. B. Kharazishvili
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A Brunn–Minkowski-Type Inequality

Geometriae Dedicata, 1999
For convex bodies \(K,L\) in \(\mathbb{R}^n\), let \(M(K,L): =\max_{x\in \mathbb{R}^n}|K\cap(x+L)|\) (where \(|\cdot|\) denotes volume). The author conjectures that \[ |K+L |^{1/n}\geq M(K,L)^{1/n} +{|K |^{1/n} |L|^{1/n}\over M(K,L)^{1/n}}, \] which would be a useful improvement of the Brunn-Minkowski theorem.
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From Brunn–Minkowski to sharp Sobolev inequalities

Annali di Matematica Pura ed Applicata, 2007
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Bobkov, S. G., Ledoux, Michel
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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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Companions to the Brunn–Minkowski inequality

Positivity
Let \(\mathcal{C}\) be the family of all compact convex sets in \(\mathbb{R}^n\). For \(A, B \in \mathcal{C}\) denote by \(\operatorname{Vol}(A)\) the Lebesque measure of \(A\) and by \(\Delta (A,B) = \big[\operatorname{Vol}(A)\big]^{1/n} + \big[\operatorname{Vol}(B)\big]^{1/n} - \big[\operatorname{Vol}(A + B)\big]^{1/n}\). An \((m + 1)\)-tuple \((B_0,
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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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