Results 81 to 90 of about 4,011 (135)

Generalizations of the Brunn–Minkowski inequality

Linear Algebra and its Applications, 2016
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New sharp Gagliardo-Nirenberg-Sobolev inequalities and an improved Borell-Brascamp-Lieb inequality [PDF]

, 2017
We propose a new Borell-Brascamp-Lieb inequality which leads to novel sharp Euclidean inequalities such as Gagliardo-Nirenberg-Sobolev inequalities in R^n and in the half-space R^n\_+.
Bolley, François, Cordero-Erausquin, Dario, Fujita, Yasuhiro, Gentil, Ivan, Guillin, Arnaud   +4 more
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Log-Brunn-Minkowski inequality under symmetry

Transactions of the American Mathematical Society, 2022
We prove the log-Brunn-Minkowski conjecture for convex bodies with symmetries to n n independent hyperplanes, and discuss the equality case and the uniqueness of the solution of the related case of the logarithmic Minkowski problem.
Böröczky, Károly J., Kalantzopoulos, Pavlos   +1 more
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Stability of the Borell–Brascamp–Lieb Inequality for Multiple Power Concave Functions

Axioms
In this paper, we prove the stability of the Brunn–Minkowski inequality for multiple convex bodies in terms of the concept of relative asymmetry. Using these stability results and the relationship of the compact support of functions, we establish the ...
Meng Qin, Zhuohua Zhang, Rui Luo, Mengjie Ren, Denghui Wu   +4 more
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Brunn–Minkowski inequality for mixed intersection bodies

Journal of Mathematical Analysis and Applications, 2005
In 1985 Lutwak introduced the notion of mixed projection bodies and obtained the Brunn-Minkowski inequality for these bodies. In this paper the authors prove the corresponding inequality for mixed intersection bodies. Besides its intrinsic interest this result is also an interesting example showing the duality between projection and intersection bodies.
Zhao, Chang-jian, Leng, Gangsong
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Brunn-Minkowski inequality for the 1-Riesz capacity and level set convexity for the 1/2-Laplacian [PDF]

, 2014
We prove that that the 1-Riesz capacity satisfi es a Brunn-Minkowski inequality, and that the capacitary function of the 1/2-Laplacian is level set convex.Comment: 9 ...
Novaga, Matteo, Ruffini, Berardo
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On Multiple $$L_p$$-Curvilinear-Brunn–Minkowski Inequalities

The Journal of Geometric Analysis
AbstractWe construct the extension of the curvilinear summation for bounded Borel measurable sets to the $$L_p$$ L p space for multiple power parameter $$\bar{\alpha }=(\alpha _1, \ldots , \alpha _{n+1})$$
Michael Roysdon, Sudan Xing
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Inequalities for dual affine quermassintegrals

Journal of Inequalities and Applications, 2006
For star bodies, the dual affine quermassintegrals were introduced and studied in several papers. The aim of this paper is to study them further. In this paper, some inequalities for dual affine quermassintegrals are established, such as the Minkowski ...
Jun Yuan, Gangsong Leng
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The polar Orlicz-Brunn-Minkowski inequalities [PDF]

Mathematical Inequalities & Applications, 2020
The Orlicz-Brunn-Minkowski theory first proposed by Lutwak, Yang and Zhang is an extension of the \(L_p\) Brunn-Minkowski theory. The Orlicz-Brunn-Minkowski inequality is a fundamental inequality in the Orlicz-Brunn-Minkowski theory which was proved respectively by \textit{R. J. Gardner} et al. [J. Differ. Geom. 97, No.
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Inequalities of Aleksandrov body

Journal of Inequalities and Applications, 2011
A new concept of p-Aleksandrov body is firstly introduced. In this paper, p-Brunn-Minkowski inequality and p-Minkowski inequality on the p-Aleksandrov body are established.
Yan Hu, Junhua Jiang
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