Results 181 to 190 of about 1,599 (218)

A quantitative isoperimetric inequality for fractional perimeters

Journal of Functional Analysis, 2011
Recently Frank and Seiringer have shown an isoperimetric inequality for nonlocal perimeter functionals arising from Sobolev seminorms of fractional order.
Nicola Fusco, Vincent Millot, Massimiliano Morini   +2 more
exaly   +2 more sources

The quantitative isoperimetric inequality and related topics [PDF]

Bulletin of Mathematical Sciences, 2015
We present some recent stability results concerning the isoperimetric inequality and other related geometric and functional inequalities.
Nicola Fusco, Fusco Nicola
exaly   +2 more sources

A quantitative isoperimetric inequality on the sphere

Advances in Calculus of Variations, 2017
In this paper we prove a quantitative version of the isoperimetric inequality on the sphere with a constant independent of the volume of the set ...
Verena Bögelein, Frank Duzaar, Nicola Fusco   +2 more
exaly   +2 more sources

A Selection Principle for the Sharp Quantitative Isoperimetric Inequality

Archive for Rational Mechanics and Analysis, 2012
We introduce a new variational method for the study of isoperimetric inequalities with quantitative terms.The method is general as it relies on a penalization technique combined with the regularity theory for quasiminimizers of the perimeter. Two notable
Marco Cicalese, Gian Paolo Leonardi, Leonardi Gian Paolo   +2 more
exaly   +2 more sources

Stability of a reverse isoperimetric inequality

Journal of Mathematical Analysis and Applications, 2009
In this note we will present a stability property of the reverse isoperimetric inequality newly obtained in [S.L. Pan, H. Zhang, A reverse isoperimetric inequality for convex plane curves, Beiträge Algebra Geom. 48 (2007) 303–308], which states that if K
Huiping Xu
exaly   +2 more sources

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Isoperimetric Inequalities and Eigenvalues

SIAM Journal on Discrete Mathematics, 1997
Summary: An upper bound is given on the minimum distance between \(i\) subsets of same size of a regular graph in terms of the \(i\)th largest eigenvalue in absolute value. This yields a bound on the diameter in terms of the \(i\)th largest eigenvalue for any integer \(i\). Our bounds are shown to be asymptotically tight for explicit families of graphs
openaire   +2 more sources

ISOPERIMETRIC INEQUALITIES FOR MULTIVARIFOLDS

Mathematics of the USSR-Izvestiya, 1986
Developing the theory of multivarifolds the author establishes new isoperimetric inequalities. The main result can be stated as follows: ''Let W be a \((k+1)\)-dimensional compact Riemannian manifold with boundary \(\partial W\), and \(g: \partial W\to R^ n\) a fixed mapping of class \(C^ r\) (resp. a locally Lipschitz mapping).
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An Isoperimetric Inequality on the Discrete Torus

SIAM Journal on Discrete Mathematics, 1990
Summary: The discrete torus is the graph on \(\mathbb{Z}^ n_ k=(\mathbb{Z}/k\mathbb{Z})^ n\) in which \(x=(x_ i)^ n_ 1\) is joined to \(y=(y_ i)^ n_ 1\) if for some \(i\) there is \(x_ i=y_ i\pm1\) and \(x_ j=y_ j\) for all \(j\neq i\). For a set \(A\subset\mathbb{Z}^ n_ k\) and a natural number \(t\), let \(A_{(t)}\) be the set of vertices of ...
Béla Bollobás, Imre Leader
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Relative isoperimetric inequality and¶linear isoperimetric inequality for minimal submanifolds

manuscripta mathematica, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An Isoperimetric Inequality for Tetrahedra

Canadian Mathematical Bulletin, 1966
Let T be a tetrahedron and let V(T) and L(T) denote its volume and the sum of its edge-lengths. In this note we prove Theorem 1. with equality if and only if the tetrahedron T is regular.
openaire   +1 more source