isoperimetric inequality


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isoperimetric inequality

[‚ī·sə‚per·ə¦me·trik ‚in·i′kwäl·əd·ē]
(mathematics)
The statement that the area enclosed by a plane curve is equal to or less than the square of its perimeter divided by 4π.
References in periodicals archive ?
The application of Bonnesen's improved isoperimetric inequality restricts many of the above arguments to the two-dimensional case.
Bonnesen (1929) improved the isoperimetric inequality for an arbitrary planar convex body K, stating that
For instance, Garnett and Jones have proved in [15] the Corona Theorem for Denjoy domains, and in [2] and [39] the authors have got characterizations of Denjoy domains which satisfy a linear isoperimetric inequality.
Topics include a review of preliminaries such as continuous and Holder continuous functions, Sobolev spaces and convex analysis; classical methods such as Euler-Lagrange equations; direct methods such as the Dirichlet integral; regularity, such as the one-dimensinal case; minimal surfaces such as in the Douglas- Courant-Tonelli method; and isoperimetric inequality.
In addition, there is an isoperimetric inequality that establishes a bound on the area in terms of the length.
We can estimate most of the density by Wirtinger's inequality; we use the isoperimetric inequality to estimate the remainder.