Results 31 to 40 of about 33,078 (239)

A Curved Brunn-Minkowski Inequality for the Symmetric Group [PDF]

, 2015
In this paper, we construct an injection $A \times B \rightarrow M \times M$ from the product of any two nonempty subsets of the symmetric group into the square of their midpoint set, where the metric is that corresponding to the conjugacy class of ...
Neeranartvong, Weerachai, Novak, Jonathan, Sothanaphan, Nat   +2 more
core   +2 more sources

The Dual Orlicz–Aleksandrov–Fenchel Inequality

Mathematics, 2020
In this paper, the classical dual mixed volume of star bodies V˜(K1,⋯,Kn) and dual Aleksandrov–Fenchel inequality are extended to the Orlicz space. Under the framework of dual Orlicz-Brunn-Minkowski theory, we put forward a new affine geometric quantity ...
Chang-Jian Zhao
doaj   +1 more source

On the concavity of the arithmetic volumes [PDF]

, 2014
In this note, we study the differentiability of the arithmetic volumes along arithmetic R-divisors, and give some equality conditions for the Brunn-Minkowski inequality for arithmetic volumes over the cone of nef and big arithmetic R-divisors.Comment: 35
Ikoma, Hideaki
core   +3 more sources

Orlicz-Aleksandrov-Fenchel Inequality for Orlicz Multiple Mixed Volumes

Journal of Function Spaces, 2018
Our main aim is to generalize the classical mixed volume V(K1,…,Kn) and Aleksandrov-Fenchel inequality to the Orlicz space. In the framework of Orlicz-Brunn-Minkowski theory, we introduce a new affine geometric quantity by calculating the Orlicz first ...
Chang-Jian Zhao
doaj   +1 more source

Geometry of normal graphs in Euclidean space and applications to the Penrose inequality in Minkowski [PDF]

, 2013
The Penrose inequality in Minkowski is a geometric inequality relating the total outer null expansion and the area of closed, connected and spacelike codimension-two surfaces S in the Minkowski spacetime, subject to an additional convexity assumption. In
Mars, Marc, Soria, Alberto
core   +1 more source

Orlicz mixed chord-integrals

AIMS Mathematics, 2020
In this paper, we introduce an affine geometric quantity and call it Orlicz mixed chord integral by defining a new Orlicz chord addition, which generalizes the mixed chord integrals to Orlicz space.
Chang-Jian Zhao
doaj   +1 more source

Geometric approaches to establish the fundamentals of Lorentz spaces $\mathbb{R}_2^3$ and $\mathbb{R}_1^2$ [PDF]

Mathematica Bohemica
The aim of this paper is to investigate the orthogonality of vectors to each other and the Gram-Schmidt method in the Minkowski space $\mathbb{R}_2^3$.
Sevilay Çoruh Şenocak, Salim Yüce
doaj   +1 more source

Some logarithmic Minkowski inequalities for nonsymmetric convex bodies and related problems

Journal of Inequalities and Applications, 2020
In this paper, we show the existence of a solution to an even logarithmic Minkowski problem for p-capacity and prove some analogue inequalities of the logarithmic Minkowski inequality for general nonsymmetric convex bodies involving p-capacity.
Lewen Ji
doaj   +1 more source

A Steiner Inequality for the Anisotropic Perimeter

Journal of Function Spaces, 2022
In this paper, we prove the monotonicity of the anisotropic perimeter of sets of finite perimeter under Steiner symmetrization by a variational formula of volume and an inequality for the anisotropic lower outer Minkowski content.
Jin Dai
doaj   +1 more source

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
doaj   +1 more source