Results 71 to 80 of about 489,827 (153)

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

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

A note on a Brunn-Minkowski inequality for the Gaussian measure [PDF]

Proceedings of the American Mathematical Society, 2013
We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.
Nayar, Piotr, Tkocz, Tomasz
openaire   +2 more sources

Stability of the Borell–Brascamp–Lieb Inequality for Multiple Power Concave Functions

Axioms
In this paper, we prove the stability of the Brunn–Minkowski inequality for multiple convex bodies in terms of the concept of relative asymmetry. Using these stability results and the relationship of the compact support of functions, we establish the ...
Meng Qin, Zhuohua Zhang, Rui Luo, Mengjie Ren, Denghui Wu   +4 more
doaj   +1 more source

On the Case of Equality in the Brunn-Minkowski Inequality for Capacity

Advances in Mathematics, 1996
Let \(\Omega_0\) and \(\Omega_1\) be convex open subsets of \(\mathbb{R}^n\) and let \(\Omega_t = \{(1 - t)x + ty : x \in \Omega_0\), \(y \in \Omega_1\}\), where \(0 \leq t \leq 1\). The Brunn-Minkowski inequality says that \[ (\text{vol} \Omega_t)^{1/N} \geq (1 - t) (\text{vol} \Omega_0)^{1/N} + t(\text{vol} \Omega_1)^{1/N}. \] \textit{C.
Caffarelli, Luis A., Jerison, David, Lieb, Elliott H.   +2 more
openaire   +2 more sources

The Reverse-log-Brunn-Minkowski inequality [PDF]

Firstly, we propose our conjectured Reverse-log-Brunn-Minkowski inequality (RLBM). Secondly, we show that the (RLBM) conjecture is equivalent to the log-Brunn-Minkowski (LBM) conjecture proposed by Böröczky-Lutwak-Yang-Zhang.
Xi, Dongmeng
core   +1 more source

Brunn–Minkowski and Zhang inequalities for convolution bodies

Advances in Mathematics, 2013
A quantitative version of Minkowski sum, extending the definition of $θ$-convolution of convex bodies, is studied to obtain extensions of the Brunn-Minkowski and Zhang inequalities, as well as, other interesting properties on Convex Geometry involving convolution bodies or polar projection bodies. The extension of this new version to more than two sets
Alonso Gutiérrez, David, Jiménez Gómez, Carlos Hugo, Villa Caro, Rafael   +2 more
openaire   +6 more sources

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  

On Brunn-Minkowski type inequality

Journal of Nonlinear Sciences and Applications, 2018
Summary: The notion of Aleksandrov body in the classical Brunn-Minkowski theory is extended to that of Orlicz-Aleksandrov body in the Orlicz Brunn-Minkowski theory. The analogs of the Brunn-Minkowski type inequality and the first variations of volume are established via Orlicz-Aleksandrov body.
Ji, Lewen, Zeng, Zhenbing, Zhong, Jingjing   +2 more
openaire   +3 more sources

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