Results 41 to 50 of about 634,955 (209)
A reverse Minkowski-type inequality
Proceedings of the American Mathematical Society, 2020 The famous Minkowski inequality provides a sharp lower bound for the mixed volume V ( K , M [ n − 1 ] ) V(K,M[n-1]) of two convex bodies K , M ⊂ R n K,M\subset \mathbb {R}^
Daniel Hug +2 more
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Indagationes Mathematicae, 2009 AbstractWe 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 bodies.
ChangJian, Z, Cheung, WS
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The log-Brunn-Minkowski inequality in $\mathbb{R}^3$ [PDF]
, 2018 B\"or\"oczky, Lutwak, Yang and Zhang recently proved the log-Brunn-Minkowski inequality which is stronger than the classical Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane. This paper establishes the log-Brunn-Minkowski, log-Minkowski, $L_p$-Minkowski and $L_p$-Brunn-Minkowski inequalities for two convex bodies in ...
arxiv +1 more source
The Minkowski inequality in de Sitter space [PDF]
Pacific Journal of Mathematics, 2021 The classical Minkowski inequality in the Euclidean space provides a lower bound on the total mean curvature of a hypersurface in terms of the surface area, which is optimal on round spheres. In this paper we employ a locally constrained inverse mean curvature flow to prove a properly defined analogue in the Lorentzian de Sitter space.
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Minkowski’s inequality for two variable difference means
, 1998 We study Minkowski’s inequality Da b(x1 + x2, y1 + y2) ≤ Da b(x1, y1) +Da b(x2, y2) (x1, x2, y1, y2 ∈ R+) and its reverse where Da b is the difference mean introduced by Stolarsky. We give necessary and sufficient conditions (concerning the parameters a,
L. Losonczi, Zsolt Páles
semanticscholar +1 more source
On a complementary Minkowski inequality
Journal of Mathematical Analysis and Applications, 1979 AbstractIt is shown that the Brunn-Minkowski inequality can be viewed as a special case of a complementary Minkowski inequality.
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Robustness of the Gaussian concentration inequality and the Brunn–Minkowski inequality [PDF]
Calculus of Variations and Partial Differential Equations, 2017 We provide a sharp quantitative version of the Gaussian concentration inequality: for every $r>0$, the difference between the measure of the $r$-enlargement of a given set and the $r$-enlargement of a half-space controls the square of the measure of the symmetric difference between the set and a suitable half-space.
Barchiesi Marco, Julin Vesa
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Solving Large‐Scale Weapon Target Assignment Problems in Seconds Using Branch‐Price‐And‐Cut
Naval Research Logistics (NRL), EarlyView.ABSTRACT This paper proposes a framework based on branch‐price‐and‐cut to solve the weapon target assignment (WTA) problem, a popular class of non‐linear assignment problems that has received significant attention over the past several decades. We first reformulate the WTA into a form amenable to column generation and then derive efficient algorithms ...
Dimitris Bertsimas, Alex Paskov
wiley +1 more source
The logarithmic Minkowski inequality for cylinders
, 2022 13 ...
Tao, Jiangyan, Xiong, Ge, Xiong, Jiawei
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Quantitative stability for the Brunn–Minkowski inequality [PDF]
Advances in Mathematics, 2017 We prove a quantitative stability result for the Brunn-Minkowski inequality: if $|A|=|B|=1$, $t \in [ ,1- ]$ with $ >0$, and $|tA+(1-t)B|^{1/n}\leq 1+ $ for some small $ $, then, up to a translation, both $A$ and $B$ are quantitatively close (in terms of $ $) to a convex set $K$.
Figalli, Alessio, Jerison, David S.
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