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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 $λ=1/2$ as the set $[A:B]_{1/2} \subseteq \mathbb{H}^2$ of all midpoints of horocycle curves connecting a point in $A$ with a point in $B$.
Rotem Assouline, Bo’az Klartag
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The dual Brunn–Minkowski inequality for log-volume of star bodies [PDF]

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
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Dual Brunn-Minkowski inequality for C-star bodies

AIMS Mathematics
In this paper, we introduced the concept of $ C $-star bodies in a fixed pointed closed convex cone $ C $ and studied the dual mixed volume for $ C $-star bodies.
Xudong Wang, Tingting Xiang
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Minkowski Inequalities via Nonlinear Potential Theory [PDF]

Archive for Rational Mechanics and Analysis, 2022
AbstractIn this paper, we prove an extended version of the Minkowski Inequality, holding for any smooth bounded set $$\Omega \subset \mathbb {R}^n$$ Ω ⊂ R n
Virginia Agostiniani, Mattia Fogagnolo, Lorenzo Mazzieri   +2 more
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On Dual Brunn-Minkowski Inequalities [PDF]

Mathematical Inequalities & Applications, 2005
On dual Brunn-Minkowski ...
Chang-Jian Zhao, ‎Josip Pečarić, Gangsong Leng   +2 more
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The log-Brunn–Minkowski inequality

Advances in Mathematics, 2012
It is conjectured that for origin-symmetric convex bodies, there exist a family of inequalities each of which is stronger than the classical Minkowski mixed-volume inequality and a family of inequalities each of which is stronger than the classical Brunn-Minkowski inequality.
Erwin Lutwak, Deane Yang, Gaoyong Zhang
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On discrete $L_p$ Brunn-Minkowski type inequalities [PDF]

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021
Abstract$$L_p$$ L p Brunn–Minkowski type inequalities for the lattice point enumerator $$\mathrm {G}_n(\cdot )$$ G n
María A. Hernández Cifre, Eduardo Lucas, Jesús Yepes Nicolás   +2 more
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Generalization of the Brunn–Minkowski Inequality in the Form of Hadwiger [PDF]

Учёные записки Казанского университета: Серия Физико-математические науки, 2016
A class of domain functionals has been built in the Euclidean space. The Brunn–Minkowski type of inequality has been applied to the said class and proved for it.
B.S. Timergaliev
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Brunn–Minkowski Inequality for $$\theta $$-Convolution Bodies via Ball’s Bodies [PDF]

J Geom Anal, 2023
David Alonso–Gutiérrez, Javier Martín Goñi   +1 more
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On Isoperimetric Inequalities in Minkowski Spaces [PDF]

Journal of Inequalities and Applications, 2010
The purpose of this expository paper is to collect some (mainly recent) inequalities, conjectures, and open questions closely related to isoperimetric problems in real, finite-dimensional Banach spaces (= Minkowski spaces).
Horst Martini, Zokhrab Mustafaev
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