Results 21 to 30 of about 543,197 (136)

Inequalities for pqth-dual mixed volumes

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023
In the paper, our main aim is to generalize the qth dual volume to Lp space, and introduce pqth-dual mixed volume by calculating the first order variation of qth dual volumes.
Zhao Chang-Jian, Bencze Mihály
doaj   +1 more source

On a geometric combination of functions related to Prékopa–Leindler inequality

Mathematika, Volume 69, Issue 2, Page 482-507, April 2023., 2023
Abstract We introduce a new operation between nonnegative integrable functions on Rn$\mathbb {R}^n$, that we call geometric combination; it is obtained via a mass transportation approach, playing with inverse distribution functions. The main feature of this operation is that the Lebesgue integral of the geometric combination equals the geometric mean ...
Graziano Crasta, Ilaria Fragalà
wiley   +1 more source

General measure extensions of projection bodies

Proceedings of the London Mathematical Society, Volume 125, Issue 5, Page 1083-1129, November 2022., 2022
Abstract The inequalities of Petty and Zhang are affine isoperimetric‐type inequalities providing sharp bounds for Volnn−1(K)Voln(Π∘K)$\text{\rm Vol}^{n-1}_{n}(K)\text{\rm Vol}_n(\Pi ^\circ K)$, where ΠK$\Pi K$ is a projection body of a convex body K$K$.
Dylan Langharst, Michael Roysdon, Artem Zvavitch   +2 more
wiley   +1 more source

On discrete $$L_p$$ Brunn–Minkowski type inequalities

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2022
Abstract$$L_p$$ L p Brunn–Minkowski type inequalities for the lattice point enumerator $$\mathrm {G}_n(\cdot )$$ G n
Hernandez Cifre, Maria A., Lucas Marín, Eduardo, Yepes Nicolás, Jesús   +2 more
openaire   +3 more sources

The Brunn-Minkowski inequality and the Heisenberg group [PDF]

, 2023
openThe core of this thesis is the Brunn-Minkowski inequality. We start proving the general version of the Brunn-Minkowski inequality in the Euclidean space, then we investigate the validity of a "geodesic" version of the Brunn-Minkowski inequality in ...
BENETTON, GIOELE
core  

A Steiner Inequality for the Anisotropic Perimeter

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 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. As a consequence, we give a more direct proof of the Wulff inequality by Steiner symmetrization.
Jin Dai, Serena Matucci
wiley   +1 more source

An Expository Lecture of María Jesús Chasco on Some Applications of Fubini’s Theorem

Axioms, 2021
The usefulness of Fubini’s theorem as a measurement instrument is clearly understood from its multiple applications in Analysis, Convex Geometry, Statistics or Number Theory. This article is an expository paper based on a master class given by the second
Alberto Castejón, María Jesús Chasco, Eusebio Corbacho, Virgilio Rodríguez de Miguel   +3 more
doaj   +1 more source

Lp‐Curvature Measures and Lp,q‐Mixed Volumes

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
Motivated by Lutwak et al.’s Lp‐dual curvature measures, we introduce the concept of Lp‐curvature measures. This new Lp‐curvature measure is an extension of the classical surface area measure, Lp‐surface area measure, and curvature measure. In this paper, we first prove some properties of the Lp‐curvature measure.
Tongyi Ma, Raúl E. Curto
wiley   +1 more source

Cyclic Brunn–Minkowski inequalities for general width and chord-integrals

Journal of Inequalities and Applications, 2019
In this paper, we establish two cyclic Brunn–Minkowski inequalities for the general ith width-integrals and general ith chord-integrals, respectively. Our works bring the cyclic inequality and Brunn–Minkowski inequality together.
Linmei Yu, Yuanyuan Zhang, Weidong Wang
doaj   +1 more source

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