Results 61 to 70 of about 137 (128)

On the Case of Equality in the Brunn-Minkowski Inequality for Capacity

Advances in Mathematics, 1996
Let \(\Omega_0\) and \(\Omega_1\) be convex open subsets of \(\mathbb{R}^n\) and let \(\Omega_t = \{(1 - t)x + ty : x \in \Omega_0\), \(y \in \Omega_1\}\), where \(0 \leq t \leq 1\). The Brunn-Minkowski inequality says that \[ (\text{vol} \Omega_t)^{1/N} \geq (1 - t) (\text{vol} \Omega_0)^{1/N} + t(\text{vol} \Omega_1)^{1/N}. \] \textit{C.
Caffarelli, Luis A., Jerison, David, Lieb, Elliott H.   +2 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
doaj   +1 more source

A note on a Brunn-Minkowski inequality for the Gaussian measure [PDF]

Proceedings of the American Mathematical Society, 2013
We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.
Nayar, Piotr, Tkocz, Tomasz
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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
doaj  

On Brunn-Minkowski type inequality

Journal of Nonlinear Sciences and Applications, 2018
Summary: The notion of Aleksandrov body in the classical Brunn-Minkowski theory is extended to that of Orlicz-Aleksandrov body in the Orlicz Brunn-Minkowski theory. The analogs of the Brunn-Minkowski type inequality and the first variations of volume are established via Orlicz-Aleksandrov body.
Ji, Lewen, Zeng, Zhenbing, Zhong, Jingjing   +2 more
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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
doaj  

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
doaj  

Functional Brunn-Minkowski inequalities induced by polarity

Advances in Mathematics, 2020
We prove a new family of inequalities, which compare the integral of a geometric convolution of non-negative functions with the integrals of the original functions. For classical inf-convolution, this type of inequality is called the Prékopa-Leindler inequality, which, restricted to indicators of convex bodies, gives the classical Brunn-Minkowski ...
Artstein-Avidan, S., Florentin, D.I., Segal, A.   +2 more
openaire   +4 more sources

The Dual Hamilton–Jacobi Equation and the Poincaré Inequality

Mathematics
Following the equivalence between logarithmic Sobolev inequalities and hypercontractivity shown by L. Gross, and applying the ideas and methods of the work by Bobkov, Gentil and Ledoux, we would like to establish a new connection between the logarithmic ...
Rigao He, Wei Wang, Jianglin Fang, Yuanlin Li   +3 more
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Sharp affine weighted L 2 Sobolev inequalities on the upper half space

Advanced Nonlinear Studies
We establish some sharp affine weighted L 2 Sobolev inequalities on the upper half space, which involves a divergent operator with degeneracy on the boundary.
Dou Jingbo, Hu Yunyun, Yue Caihui
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