Results 71 to 80 of about 4,011 (135)

Some Brunn-Minkowski type inequalities for L p $L_{p}$ radial Blaschke-Minkowski homomorphisms

Journal of Inequalities and Applications, 2016
Schuster introduced radial Blaschke-Minkowski homomorphisms. Recently, they were generalized to L p $L_{p}$ radial Blaschke-Minkowski homomorphisms by Wang et al.
Ying Zhou, Weidong Wang
doaj   +1 more source

New fiber and graph combinations of convex bodies

Mathematika, Volume 71, Issue 4, October 2025.
Abstract Three new combinations of convex bodies are introduced and studied: the Lp$L_p$ fiber, Lp$L_p$ chord, and graph combinations. These combinations are defined in terms of the fibers and graphs of pairs of convex bodies, and each operation generalizes the classical Steiner symmetral, albeit in different ways.
Steven Hoehner, Sudan Xing
wiley   +1 more source

Isoperimetric and Functional Inequalities

Моделирование и анализ информационных систем, 2018
We establish lower estimates for an integral functional$$\int\limits_\Omega f(u(x), \nabla u(x)) \, dx ,$$where \(\Omega\) -- a bounded domain in \(\mathbb{R}^n \; (n \geqslant 2)\), an integrand \(f(t,p) \, (t \in [0, \infty),\; p \in \mathbb{R}^n)\) --
Vladimir S. Klimov
doaj   +1 more source

The sharp doubling threshold for approximate convexity

Bulletin of the London Mathematical Society, Volume 56, Issue 10, Page 3229-3239, October 2024.
Abstract We show for A,B⊂Rd$A,B\subset \mathbb {R}^d$ of equal volume and t∈(0,1/2]$t\in (0,1/2]$ that if |tA+(1−t)B|<(1+td)|A|$|tA+(1-t)B|< (1+t^d)|A|$, then (up to translation) |co(A∪B)|/|A|$|\operatorname{co}(A\cup B)|/|A|$ is bounded. This establishes the sharp threshold for the quantitative stability of the Brunn–Minkowski inequality recently ...
Peter van Hintum, Peter Keevash
wiley   +1 more source

Multigraded algebras and multigraded linear series

Journal of the London Mathematical Society, Volume 109, Issue 3, March 2024.
Abstract This paper is devoted to the study of multigraded algebras and multigraded linear series. For an Ns$\mathbb {N}^s$‐graded algebra A$A$, we define and study its volume function FA:N+s→R$F_A:\mathbb {N}_+^s\rightarrow \mathbb {R}$, which computes the asymptotics of the Hilbert function of A$A$. We relate the volume function FA$F_A$ to the volume
Yairon Cid‐Ruiz, Fatemeh Mohammadi, Leonid Monin   +2 more
wiley   +1 more source

Horocyclic Brunn-Minkowski inequality

Advances in Mathematics
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 $B$.
Assouline, Rotem, Klartag, Bo'az
openaire   +3 more sources

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

L_p Radial Blaschke-Minkowski Homomorphisms and L_p Dual Affine Surface Areas

Mathematics, 2019
Schuster introduced the notion of radial Blaschke-Minkowski homomorphism and considered the Busemann-Petty problem for volume forms. Whereafter, Wang, Liu and He presented the L p radial Blaschke-Minkowski homomorphisms and extended Schuster ...
Zhonghuan Shen, Weidong Wang
doaj   +1 more source

Concavity properties for free boundary elliptic problems

, 2010
We prove some concavity properties connected to nonlinear Bernoulli type free boundary problems. In particular, we prove a Brunn-Minkowski inequality and an Urysohn's type inequality for the Bernoulli Constant and we study the behaviour of the free ...
Bianchini, C., Salani, P.
core   +1 more source

Forward and Reverse Entropy Power Inequalities in Convex Geometry

, 2016
The entropy power inequality, which plays a fundamental role in information theory and probability, may be seen as an analogue of the Brunn-Minkowski inequality.
Madiman, Mokshay, Melbourne, James, Xu, Peng   +2 more
core   +1 more source