Results 31 to 40 of about 489,757 (102)
A nonabelian Brunn-Minkowski inequality [PDF]
, 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
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Discrepancy of arithmetic progressions in boxes and convex bodies
Mathematika, Volume 72, Issue 2, April 2026.Abstract The combinatorial discrepancy of arithmetic progressions inside [N]:={1,…,N}$[N]:= \lbrace 1, \ldots, N\rbrace$ is the smallest integer D$D$ for which [N]$[N]$ can be colored with two colors so that any arithmetic progression in [N]$[N]$ contains at most D$D$ more elements from one color class than the other.
Lily Li, Aleksandar Nikolov
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Stability of reverse isoperimetric inequalities in the plane: Area, Cheeger, and inradius
Bulletin of the London Mathematical Society, Volume 58, Issue 2, February 2026.Abstract In this paper, we present stability results for various reverse isoperimetric problems in R2$\mathbb {R}^2$. Specifically, we prove the stability of the reverse isoperimetric inequality for λ$\lambda$‐convex bodies — convex bodies with the property that each of their boundary points p$p$ supports a ball of radius 1/λ$1/\lambda$ so that the ...
Kostiantyn Drach, Kateryna Tatarko
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, 2020 Communications on Pure and Applied Mathematics, Volume 73, Issue 7, Page 1406-1452, July, 2020.
Károly J. Böröczky +4 more
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Inequalities and counterexamples for functional intrinsic volumes and beyond
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract We show that analytic analogs of Brunn–Minkowski‐type inequalities fail for functional intrinsic volumes on convex functions. This is demonstrated both through counterexamples and by connecting the problem to results of Colesanti, Hug, and Saorín Gómez.
Fabian Mussnig, Jacopo Ulivelli
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Sharp quantitative stability of the Brunn-Minkowski inequality [PDF]
, 2023 The Brunn-Minkowski inequality states that for bounded measurable sets $A$ and $B$ in $\mathbb{R}^n$, we have $|A+B|^{1/n} \geq |A|^{1/n}+|B|^{1/n}$. Also, equality holds if and only if $A$ and $B$ are convex and homothetic sets in $\mathbb{R}^d$.
van Hintum, Peter +2 more
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Generalization of the Brunn–Minkowski Inequality in the Form of Hadwiger [PDF]
Учёные записки Казанского университета: Серия Физико-математические науки, 2016 A class of domain functionals has been built in the Euclidean space. The Brunn–Minkowski type of inequality has been applied to the said class and proved for it.
B.S. Timergaliev
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Some Brunn-Minkowski type inequalities for L p $L_{p}$ radial Blaschke-Minkowski homomorphisms
Journal of Inequalities and Applications, 2016 Schuster introduced radial Blaschke-Minkowski homomorphisms. Recently, they were generalized to L p $L_{p}$ radial Blaschke-Minkowski homomorphisms by Wang et al.
Ying Zhou, Weidong Wang
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Journal of Mathematics, Volume 2026, Issue 1, 2026.In this paper, we established a sharp integral inequality involving the Chebyshev functional and the average of Riemann integrable functions. Our main result furnishes a refined upper bound with the best possible constant, unifying and extending some classical inequalities (Hölder, Cauchy–Schwarz, Ostrowski, trapezoidal, and Simpson).
Mohsen Rostamian Delavar +2 more
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The Brunn-Minkowski inequality [PDF]
, 2002 . In 1978, Osserman [124] wrote a rather comprehensive survey on the isoperimetric inequality. The Brunn-Minkowski inequality can be proved in a page, yet quickly yields the classical isoperimetric inequality for important classes of subsets of R n, and ...
Gardner, Richard J., R. J. Gardner
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