Results 41 to 50 of about 503,781 (127)
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
Gaussian Brunn-Minkowski Inequalities [PDF]
, 2010 A detailed investigation is undertaken into Brunn-Minkowski-type inequalities for Gauss measure. A Gaussian dual Brunn-Minkowski inequality, the first of its type, is proved, together with precise equality conditions, and is shown to be the best possible
Zvavitch, Artem, Gardner, Richard J.
core
, 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, ChangJian, Z
core +1 more source
A direct proof of the Brunn-Minkowski inequality in nilpotentLie groups [PDF]
, 2022 The author would like to thank his Ph.D. advisor Manuel Ritoré for sugesting the problem and his helpThe purpose of this work is to give a direct proof of the multiplicative Brunn-Minkowski inequality in nilpotent Lie groups based on Hadwiger-Ohmann’s ...
Pozuelo Domínguez, Julián +1 more
core +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
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
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 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
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
Brunn-Minkowski inequality and its aftermath. [PDF]
, 1978 1 online resource (PDF, 33 pages)Das Gupta, Somesh. (1978). Brunn-Minkowski inequality and its aftermath..
Das Gupta, Somesh
core