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The Functional Orlicz Brunn-Minkowski Inequality for q-Capacity

Journal of Function Spaces, 2020
In this paper, we establish functional forms of the Orlicz Brunn-Minkowski inequality and the Orlicz-Minkowski inequality for the electrostatic q-capacity, which generalize previous results by Zou and Xiong.
Wei Wang, Juan Li, Rigao He, Lijuan Liu
doaj   +3 more sources

A nonabelian Brunn–Minkowski inequality [PDF]

Geometric and Functional Analysis, 2021
Henstock and Macbeath asked in 1953 whether the Brunn–Minkowski inequality can be generalized to nonabelian locally compact groups; questions along the same line were also asked by Hrushovski, McCrudden, and Tao.
Yi-Fan Jing, Chieu-Minh Tran, Ruixiang Zhang   +2 more
semanticscholar   +5 more sources

The dual Brunn–Minkowski inequality for log-volume of star bodies

Journal of Inequalities and Applications, 2021
This paper aims to consider the dual Brunn–Minkowski inequality for log-volume of star bodies, and the equivalent Minkowski inequality for mixed log-volume.
Dandan Lai, Hailin Jin
doaj   +2 more sources

The Minkowski inequality involving generalized k-fractional conformable integral

Journal of Inequalities and Applications, 2019
In the research paper, the authors exploit the definition of a new class of fractional integral operators, recently proposed by Jarad et al. (Adv. Differ. Equ.
Shahid Mubeen, Siddra Habib, Muhammad Nawaz Naeem   +2 more
doaj   +2 more sources

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   +2 more sources

Minkowski inequality on complete Riemannian manifolds with nonnegative Ricci curvature [PDF]

Analysis & PDE, 2021
In this paper we consider Riemannian manifolds of dimension at least $3$, with nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset with smooth boundary we establish the validity of an optimal Minkowski Inequality.
L. Benatti, Mattia Fogagnolo, L. Mazzieri   +2 more
semanticscholar   +1 more source

The Brunn–Minkowski inequality implies the CD condition in weighted Riemannian manifolds [PDF]

Nonlinear Analysis, 2022
The curvature dimension condition CD(K,N), pioneered by Sturm and Lott--Villani, is a synthetic notion of having curvature bounded below and dimension bounded above, in the non-smooth setting. This condition implies a suitable generalization of the Brunn-
Mattia Magnabosco, Lorenzo Portinale, Tommaso Rossi   +2 more
semanticscholar   +1 more source

Horocyclic Brunn-Minkowski inequality [PDF]

Advances in Mathematics, 2022
Given two non-empty subsets $A$ and $B$ of the hyperbolic plane $\mathbb{H}^2$, we define their horocyclic Minkowski sum with parameter $\lambda=1/2$ as the set $[A:B]_{1/2} \subseteq \mathbb{H}^2$ of all midpoints of horocycle curves connecting a point ...
Rotem Assouline, B. Klartag
semanticscholar   +1 more source

Minkowski inequality for nearly spherical domains [PDF]

Advances in Mathematics, 2021
We investigate the validity and the stability of various Minkowski-like inequalities for C-perturbations of the ball. Let K ⊆ R be a domain (possibly not convex and not mean-convex) which is C-close to a ball.
F. Glaudo
semanticscholar   +1 more source

The dimensional Brunn–Minkowski inequality in Gauss space [PDF]

Journal of Functional Analysis, 2020
Let $\gamma_n$ be the standard Gaussian measure on $\mathbb{R}^n$. We prove that for every symmetric convex sets $K,L$ in $\mathbb{R}^n$ and every $\lambda\in(0,1)$, $$\gamma_n(\lambda K+(1-\lambda)L)^{\frac{1}{n}} \geq \lambda \gamma_n(K)^{\frac{1}{n}}+(
Alexandros Eskenazis, Georgios Moschidis
semanticscholar   +1 more source