Results 71 to 80 of about 2,936 (172)

Generalizations of the Brunn–Minkowski inequality

Linear Algebra and its Applications, 2016
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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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L_p Radial Blaschke-Minkowski Homomorphisms and L_p Dual Affine Surface Areas

Mathematics, 2019
Schuster introduced the notion of radial Blaschke-Minkowski homomorphism and considered the Busemann-Petty problem for volume forms. Whereafter, Wang, Liu and He presented the L p radial Blaschke-Minkowski homomorphisms and extended Schuster ...
Zhonghuan Shen, Weidong Wang
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On Gaussian Brunn-Minkowski inequalities

, 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 allows us to have semigroup proofs of the geometric Brascamp-Lieb inequality and of the reverse one
Barthe, Franck, Huet, Nolwen
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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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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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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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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 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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On Minkowski's inequality and its application

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
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