Results 21 to 30 of about 1,599 (218)

Torsional rigidity on compact Riemannian manifolds with lower Ricci curvature bounds

Open Mathematics, 2015
In this article we prove a reverse Hölder inequality for the fundamental eigenfunction of the Dirichlet problem on domains of a compact Riemannian manifold with lower Ricci curvature bounds.
Gamara Najoua, Hasnaoui Abdelhalim, Makni Akrem   +2 more
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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

LOW-DEGREE BOOLEAN FUNCTIONS ON $S_{n}$ , WITH AN APPLICATION TO ISOPERIMETRY

Forum of Mathematics, Sigma, 2017
We prove that Boolean functions on $S_{n}$ , whose Fourier transform is highly concentrated on irreducible representations indexed by partitions of
DAVID ELLIS, YUVAL FILMUS, EHUD FRIEDGUT
doaj   +1 more source

A sharp relative isoperimetric inequality for the square

Comptes Rendus. Mathématique, 2021
We compute the exact value of the least “relative perimeter” of a shape $S$, with a given area, contained in a unit square; the relative perimeter of $S$ being the length of the boundary of $S$ that does not touch the border of the square.
Brezis, Haim, Bruckstein, Alfred
doaj   +1 more source

Isoperimetric Inequality for Disconnected Regions

, 2021
The discrete isoperimetric inequality in Euclidean geometry states that among all $n$-gons having a fixed perimeter $p$, the one with the largest area is the regular $n$-gon.
Sanki, Bidyut, Vadnere, Arya
core   +1 more source

The Isoperimetric Inequality

Notices of the American Mathematical Society
The isoperimetric problem is one of the oldest and most famous problems in geometry.
Eichmair, Michael, Brendle, Simon
openaire   +3 more sources

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
doaj   +1 more source

Edge-Isoperimetric Inequalities and Influences [PDF]

Combinatorics, Probability and Computing, 2007
We give a combinatorial proof of the result of Kahn, Kalai and Linial [16], which states that every balanced boolean function on the n-dimensional boolean cube has a variable with influence of at least $\Omega\bigl(\frac{\log n}{n}\bigr)$ .
Dvir Falik, Alex Samorodnitsky
openaire   +3 more sources

Log-Minkowski inequalities for the Lp $L_{p}$-mixed quermassintegrals

Journal of Inequalities and Applications, 2019
Böröczky et al. proposed the log-Minkowski problem and established the plane log-Minkowski inequality for origin-symmetric convex bodies. Recently, Stancu proved the log-Minkowski inequality for mixed volumes; Wang, Xu, and Zhou gave the Lp $L_{p ...
Chao Li, Weidong Wang
doaj   +1 more source

Isoperimetric inequalities in simplicial complexes [PDF]

Combinatorica, 2015
In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and prove that similar connections exist between the combinatorial expansion of a complex, and the spectrum of the high ...
Ori Parzanchevski, Ron Rosenthal, Ran J. Tessler   +2 more
openaire   +2 more sources