Results 41 to 50 of about 654,419 (234)
Isoperimetric and Brunn-Minkowski inequalities for the (p, q)-mixed geominimal surface areas
Open Mathematics, 2022 Motivated by the celebrated work of Lutwak, Yang and Zhang [1] on (p,q)\left(p,q)-mixed volumes and that of Feng and He [2] on (p,q)\left(p,q)-mixed geominimal surface areas, we in the present paper establish and confirm the affine isoperimetric and ...
Zhang Juan, Wang Weidong, Zhao Peibiao
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Bonnesen-style symmetric mixed inequalities
Journal of Inequalities and Applications, 2016 In this paper, we investigate the symmetric mixed isoperimetric deficit Δ 2 ( K 0 , K 1 ) $\Delta_{2}(K_{0},K_{1})$ of domains K 0 $K_{0}$ and K 1 $K_{1}$ in the Euclidean plane R 2 $\mathbb{R}^{2}$ .
Pengfu Wang, Miao Luo, Jiazu Zhou
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Extension of two inequalities of payne
Journal of Inequalities and Applications, 1997 In this note isoperimetric bounds are derived for the maximum of the solution to the Poisson problem for a plane domain. This extends previous bounds of Payne valid for the torsion problem.
Sperb R
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Optimal isoperimetric inequalities for surfaces in any codimension in Cartan-Hadamard manifolds [PDF]
Geometric and Functional Analysis, 2018 Let $$(M^n,g)$$ ( M n , g ) be simply connected, complete, with non-positive sectional curvatures, and $$\Sigma $$ Σ a 2-dimensional closed integral current (or flat chain mod 2) with compact support in M . Let S be an area minimising integral 3-current (
F. Schulze
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Estimates for capacities and traces of potentials
International Journal of Mathematics and Mathematical Sciences, 1984 It is shown that isoperimetric inequalities, relating measures and capacities, hold for all sets in ℝn if they are valid for all balls. As a corollary, the necessary and sufficient conditions for the continuity of some imbeddings of M. Riesz and Bessel
V. G. Maz'ja, S. P. Preobrazenskii
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International mathematics research notices, 2019 A new affine invariant geometric functional for convex polytopes is introduced. Some new sharp affine isoperimetric inequalities are established for this new functional, which are extensions of Lutwak–Yang–Zhang’s results on their celebrated cone ...
Jiaqi Hu, Ge Xiong
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Higher order Wirtinger-type inequalities and sharp bounds for the isoperimetric deficit [PDF]
Proceedings of the American Mathematical Society, 2020 Using Fourier analysis, we derive Wirtinger-type inequalities of arbitrary high order. As applications, we prove various sharp geometric inequalities for closed curves on the Euclidean plane. In particular, we obtain both sharp lower and upper bounds for
Kwok-Kun Kwong, Hojoo Lee
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On weighted isoperimetric inequalities with non-radial densities [PDF]
Applicable Analysis, 2018 We consider a class of isoperimetric problems on , where the volume and the area element carry two different weights of the type . We solve them in a special case while a more detailed study is contained in Alvino et al.
A. Alvino +4 more
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An Expository Lecture of María Jesús Chasco on Some Applications of Fubini’s Theorem
Axioms, 2021 The usefulness of Fubini’s theorem as a measurement instrument is clearly understood from its multiple applications in Analysis, Convex Geometry, Statistics or Number Theory. This article is an expository paper based on a master class given by the second
Alberto Castejón +3 more
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Isoperimetric and Concentration Inequalities - Equivalence under Curvature Lower Bound
, 2009 It is well known that isoperimetric inequalities imply in a very general measure-metric-space setting appropriate concentration inequalities. The former bound the boundary measure of sets as a function of their measure, whereas the latter bound the ...
Milman, Emanuel
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