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On Isoperimetric Inequalities in Minkowski Spaces
Journal of Inequalities and Applications, 2010 The purpose of this expository paper is to collect some (mainly recent) inequalities, conjectures, and open questions closely related to isoperimetric problems in real, finite-dimensional Banach spaces (= Minkowski spaces).
Mustafaev Zokhrab, Martini Horst
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Isoperimetric inequalities of the fourth order Neumann eigenvalues
Journal of Inequalities and Applications, 2020 In this paper, we obtain some isoperimetric inequalities for the first ( n − 1 ) $(n-1)$ eigenvalues of the fourth order Neumann Laplacian on bounded domains in an n-dimensional Euclidean space. Our result supports strongly the conjecture of Chasman.
Yanlin Deng, Feng Du
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Weighted isoperimetric inequalities in cones and applications [PDF]
, 2012 This paper deals with weighted isoperimetric inequalities relative to cones of $\mathbb{R}^{N}$. We study the structure of measures that admit as isoperimetric sets the intersection of a cone with balls centered at the vertex of the cone.
Brock, Friedemann +2 more
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Isoperimetric inequalities for some nonlinear eigenvalue problems
Electronic Journal of Qualitative Theory of Differential Equations, 2004 In this paper we intend to review many of the known inequalities for eigenvalues of the Laplacian in Euclidean plane. Our aim is to show that we can generalize some results for the pseudo-Laplacian.
Gabriella Bognár
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Dilation Type Inequalities for Strongly-Convex Sets in Weighted Riemannian Manifolds
Analysis and Geometry in Metric Spaces, 2021 In this paper, we consider a dilation type inequality on a weighted Riemannian manifold, which is classically known as Borell’s lemma in high-dimensional convex geometry.
Tsuji Hiroshi
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An Asymptotic Isoperimetric Inequality [PDF]
Geometric And Functional Analysis, 1998 For a finite metric space \(V\) with a metric \(\rho\) and probability measure \(\mu\), let \(V^n\) be the product metric space in which the distance between \(a= (a_1,\dots, a_n)\) and \(b= (b_1,\dots, b_n)\) is \(\rho_n(a,b)= \sum_i\rho(a_i, b_i)\) and the measure \(\mu_n(a_1,\dots, a_n)= \prod_i\mu(a_i)\). For any \(d\geq 0\) the \(d\)-neighbourhood
Alon, N., Boppana, R., Spencer, J.
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Affine vs. Euclidean isoperimetric inequalities [PDF]
Advances in Mathematics, 2018 It is shown that every even, zonal measure on the Euclidean unit sphere gives rise to an isoperimetric inequality for sets of finite perimeter which directly implies the classical Euclidean isoperimetric inequality.
Christoph Haberl, Franz E. Schuster
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Dual Lp-Mixed Geominimal Surface Area and Related Inequalities
Journal of Function Spaces, 2016 The integral formula of dual Lp-geominimal surface area is given and the concept of dual Lp-geominimal surface area is extended to dual Lp-mixed geominimal surface area. Properties for the dual Lp-mixed geominimal surface areas are established.
Tongyi Ma, Yibin Feng
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Isoperimetric inequalities for -Hessian equations
Advances in Nonlinear Analysis, 2012 We consider the homogeneous Dirichlet problem for a special -Hessian equation of sub-linear type in a -convex domain , . We study the comparison between the solution of this problem and the (radial) solution of the corresponding problem in a ball having ...
Mohammed Ahmed +2 more
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Holography, probe branes and isoperimetric inequalities
Physics Letters B, 2015 In many instances of holographic correspondences between a d-dimensional boundary theory and a (d+1)-dimensional bulk, a direct argument in the boundary theory implies that there must exist a simple and precise relation between the Euclidean on-shell ...
Frank Ferrari, Antonin Rovai
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