Results 41 to 50 of about 813 (131)
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 +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
Lp Radial Blaschke-Minkowski Homomorphisms and Lp 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
Brunn–Minkowski inequality for mixed intersection bodies
, 2005 Dual of the Brunn–Minkowski inequality for mixed projection bodies are established for mixed intersection ...
Zhao, Chang-jian, Leng, Gangsong
core +1 more source
, 2009 We introduce the notion of Lp-mixed intersection body (p < 1) and extend the classical notion dual mixed volume to an Lp setting. Further, we establish the Brunn-Minkowski inequality for the q-dual mixed volumes of star duals of Lp-mixed intersection ...
Cheung, WS +3 more
core +1 more source
Stability of the Borell–Brascamp–Lieb Inequality for Multiple Power Concave Functions
AxiomsIn 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 +4 more
doaj +1 more source
A nonabelian Brunn-Minkowski inequality
, 2023 Henstock and Macbeath asked in 1953 whether the Brunn-Minkowski inequality can be generalized to nonabelian locally compact groups; questions along the same line were also asked by Hrushovski, McCrudden, and Tao.
Jing, Yifan +2 more
core +1 more source
Stability of inequalities in the dual Brunn-Minkowski theory
, 1999 Stability versions are given of several inequalities from E. Lutwak's dual Brunn-Minkowski theory. These include the dual Aleksandrov-Fenchel inequality, the dual Brunn-Minkowski inequality, and the dual isoperimetric inequality. Two methods are used.
Vassallo, Salvatore Flavio
core +2 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
The log-Brunn–Minkowski inequality
, 2012 For origin-symmetric convex bodies (i.e., the unit balls of finite dimensional Banach spaces) it is conjectured that there exist a family of inequalities each of which is stronger than the classical Brunn–Minkowski inequality and a family of inequalities
Lutwak, Erwin +7 more
core +1 more source