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The General Minkowski Inequality for Mixed Volume
Journal of Function Spaces, Volume 2024, Issue 1, 2024.Mixed volume is an important notion in convex geometry, which is the extension of volume and surface area. The Minkowski inequality for mixed volume plays a vital role in convex geometry. This paper obtains that mixed volume under Steiner symmetrization is monotonic and decreasing, and a concise proof of the general Minkowski inequality by Steiner ...
Yusha Lv, Yoshihiro Sawano
wiley +1 more source
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
A Brunn-Minkowski Type Theorem on the Minkowski Spacetime
, 1999 In this article, we derive a Brunn-Minkowski type theorem for sets bearing some relation to the causal structure on the Minkowski spacetime . We also present an isoperimetric inequality in the Minkowski spacetime as a consequence of this Brunn-Minkowski
Hyoungsick Bahn, Paul Ehrlich
core +1 more source
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
Gaussian Brunn-Minkowski inequalities
, 2020 . A detailed investigation is undertaken into Brunn-Minkowski-type inequalities for Gauss measure. A Gaussian dual Brunn-Minkowski inequality is proved, together with precise equality conditions, and shown to be best possible from several points of view.
Artem Zvavitch, Richard J Gardner
core
Orlicz Dual Brunn-Minkowski Theory: Addition, Dual Quermassintegrals, and Inequalities
, 2018 We further consider the Orlicz dual Brunn-Minkowski theory. An Orlicz radial harmonic addition is introduced, which generalizes the Lp-radial addition and the Lp-harmonic addition to an Orlicz space, respectively.
Zhao, C +3 more
core +1 more source
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
Orlicz-Brunn-Minkowski inequality for radial Blaschke-Minkowski homomorphisms
, 2018 In this paper, we extend the Brunn-Minkowski inequality for radial Blaschke-Minkowski homomorphisms to an Orlicz setting and an Orlicz-Brunn- Minkowski inequality for radial Blaschke-Minkowski homomorphisms is established.
Zhao, Chang-Jian
core
Robustness of the Gaussian concentration inequality and the Brunn-Minkowski inequality [PDF]
, 2017 We provide a sharp quantitative version of the Gaussian concentration inequality: for every $r>0$, the difference between the measure of the $r$-enlargement of a given set and the $r$-enlargement of a half-space controls the square of the measure of ...
BARCHIESI, MARCO +5 more
core +1 more source
The Dual Hamilton–Jacobi Equation and the Poincaré Inequality
MathematicsFollowing 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 +3 more
doaj +1 more source