Results 61 to 70 of about 543,197 (136)

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

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

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

The Brunn–Minkowski–Firey inequality for nonconvex sets

Advances in Applied Mathematics, 2012
In this short note, the authors first extend the definition of Minkowski-Firey \(L_p\)-combinations from convex bodies to arbitrary subsets of Euclidean space, and then prove the Brunn-Minkowski-Firey inequality for compact (not necessarily convex) sets of \(\mathbb{R}^n\).
Erwin Lutwak, Deane Yang, Gaoyong Zhang
openaire   +2 more sources

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

On a complementary Minkowski inequality

, 1979
It is shown that the Brunn-Minkowski inequality can be viewed as a special case of a complementary Minkowski ...
Lutwak, Erwin
core   +1 more source

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

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

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

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