On the quantitative isoperimetric inequality in the plane

DOI10.1051/cocv/2016002zbMath1456.49034arXiv1507.08189OpenAlexW1637818975MaRDI QIDQ2968796

Gisella Croce, Chiara Bianchini, Antoine Henrot

Publication date: 22 March 2017

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.08189

zbMATH Keywords

optimality conditionsisoperimetric inequalityrearrangementFraenkel asymmetryisoperimetric deficitquantitative isoperimetric inequalityshape derivative

Mathematics Subject Classification ID

Set-valued and variational analysis (49J53) Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) Length, area, volume, other geometric measure theory (28A75) Optimization of shapes other than minimal surfaces (49Q10)

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Cites Work

• Unnamed Item
• A sharp isoperimetric inequality in the plane
• The quantitative isoperimetric inequality and related topics
• A mass transportation approach to quantitative isoperimetric inequalities
• A sharp isoperimetric inequality in the plane involving Hausdorff distance
• On asymmetry and capacity
• Isoperimetric deficit and convex plane sets of maximum translative discrepancy
• A problem in the theory of subordination
• A selection principle for the sharp quantitative isoperimetric inequality
• Best constants for the isoperimetric inequality in quantitative form
• An analytic proof of the planar quantitative isoperimetric inequality
• The sharp quantitative isoperimetric inequality
• Variation and optimization of formes. A geometric analysis
• Some methods for studying stability in isoperimetric type problems

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