# Quantitative isoperimetric inequalities for a class of nonconvex sets

## Related Articles

- Relative Isoperimetric Inequality for Minimal Submanifolds in a Riemannian Manifold. Juncheol Pyo // Journal of Inequalities & Applications;2010, Vol. 2010, p1
Let Î£ be a domain on an m-dimensional minimal submanifold in the outside of a convex set C in Sn or Hn. The modified volume M(Î£) is introduced by Choe and Gulliver (1992) and we prove a sharp modified relative isoperimetric inequality for the domain Î£, (1/2)mm?mM(Î£)m-1 â©½...

- A Selection Principle for the Sharp Quantitative Isoperimetric Inequality. Cicalese, Marco; Leonardi, Gian // Archive for Rational Mechanics & Analysis;Nov2012, Vol. 206 Issue 2, p617
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 applications are presented. First we...

- Optimal convex shapes for concave functionals. Bucur, Dorin; Fragalà, Ilaria; Lamboley, Jimmy // ESAIM: Control, Optimisation & Calculus of Variations;Jul2012, Vol. 18 Issue 3, p693
Motivated by a long-standing conjecture of PÃ³lya and SzegÃ¶ about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We...

- A strong form of the quantitative isoperimetric inequality. Fusco, Nicola; Julin, Vesa // Calculus of Variations & Partial Differential Equations;Jul2014, Vol. 50 Issue 3/4, p925
We give a refinement of the quantitative isoperimetric inequality. We prove that the isoperimetric gap controls not only the Fraenkel asymmetry but also the oscillation of the boundary.

- A quantitative estimate for mappings of bounded inner distortion. Farroni, Fernando; Moscariello, Gioconda // Calculus of Variations & Partial Differential Equations;Nov2014, Vol. 51 Issue 3/4, p657
We establish a quantitative version of distortion inequality for mappings of bounded inner distortion. Some applications to the integral form of the isoperimetric inequality are given.

- FACTORABLE GENERALIZED HAUSDORFF MATRICES. Akgun, F. Aydin; Rhoades, B. E. // Journal of Advanced Mathematical Studies;Jan2010, Vol. 3 Issue 1, p1
We determine necessary and sufficient conditions for a conservative generalized Hausdorff matrix to be factorable.

- Relations entre isopÃ©rimÃ©trie et trou spectral pour les chaÃ®nes de Markov finies. Miclo, Laurent // Probability Theory & Related Fields;1999, Vol. 114 Issue 4
Abstract. Let G be a finite and connected graph, we will note by l(G) the maximum length of an injective path in G. We will show (by two dictinct proofs, one using sub-trees of G and the other based on multiflows of paths) that sup[sub (P, mu)is an element of R(G)] I (P, mu)/lambda(P, mu) =...

- An isoperimetric inequality related to Thue's equation. Bean, Michael A. // Bulletin (New Series) of the American Mathematical Society;Oct1994, Vol. 31 Issue 2, p204
Announces the discovery of an isoperimetric inequality for the plane-region area defined by binary forms. Application to the enumeration of solutions to Thue inequality; Future applications.

- Local Stability Study of Mamdani Fuzzy PI Control Systems Determination of an Attraction Domain. Zahra, B.; Sakly, A.; Benrejeb, M. // International Review of Automatic Control;May2009, Vol. 2 Issue 3, p258
The determination of an attraction domain of an equilibrium point for fuzzy PI control systems in the case of particular partition of fuzzy input subsets is developed in this paper. To search local asymptotic stability for the fuzzy system, homogeneous overvaluing systems and the arrow form of...