Results 21 to 30 of about 1,372 (214)
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
doaj +2 more sources
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
doaj +1 more source
Randomized Isoperimetric Inequalities [PDF]
, 2017 We discuss isoperimetric inequalities for convex sets. These include the classical isoperimetric inequality and that of Brunn-Minkowski, Blaschke-Santalo, Busemann-Petty and their various extensions. We show that many such inequalities admit stronger randomized forms in the following sense: for natural families of associated random convex sets one has ...
Paouris, Grigoris, Pivovarov, Peter
openaire +2 more sources
Symmetrization inequalities for probability metric spaces with convex isoperimetric profile [PDF]
, 2020 We obtain symmetrization inequalities on probability metric spaces with convex isoperimetric profile which incorporate in their formulation the isoperimetric estimator and that can be applied to provide a unified treatment of sharp Sobolev-Poincare and ...
Walter A. Ortiz +5 more
core +1 more source
Compressions and isoperimetric inequalities
Journal of Combinatorial Theory, Series A, 1991 Let \(G=(V,E)\) be a graph. For \(A\subset V\) and \(y\in V\), set \(D(A,y)=\inf \{d(x,y):\) \(x\in A\}\), where d is the usual graph metric. For \(t=0,1,2,...\), \(A_{(t)}=\{y\in V:\) d(A,y)\(\leq t\}\) is the t-boundary of A and \(A_{(1)}=\partial A\) is the boundary of A.
Béla Bollobás, Imre Leader
openaire +2 more sources
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
doaj +1 more source
Edge isoperimetric inequalities for product graphs [PDF]
, 2000 It is well known that there is a simple equivalence between isoperimetric inequalities and certain analytic inequalities in Riemannian manifolds (see Rothaus, J. Funct. Anal. 64 (1985) 296–313).
Tillich, Jean-Pierre +1 more
core +1 more source
Quantitative isoperimetric inequalities in H^n [PDF]
, 2015 In the Heisenberg group H^n we prove quantitative isoperimetric inequalities for Pansu's spheres, that are known to be isoperimetric under various assumptions.
LEONARDI, Gian Paolo +2 more
core +1 more source
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
doaj +1 more source
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
doaj +1 more source