A sharp isoperimetric inequality in the plane involving Hausdorff distance

DOI10.4171/RLM/555zbMath1182.52008MaRDI QIDQ1039880

Carlo Nitsch, Angelo Alvino, Vincenzo Ferone

Publication date: 23 November 2009

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: http://www.ems-ph.org/journals/show_abstract.php?issn=1120-6330&vol=20&iss=4&rank=8

zbMATH Keywords

isoperimetric inequalityHausdorff distanceisoperimetric deficitcircular symmetrizationBonnesen-style inequalitysymmetric lensHausdorff asymmetry index

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Optimization of shapes other than minimal surfaces (49Q10) Convex sets in (2) dimensions (including convex curves) (52A10)

Related Items (4)

Stability results for some fully nonlinear eigenvalue estimates ⋮ On the quantitative isoperimetric inequality in the plane ⋮ Sharp quantitative isoperimetric inequalities in the 𝐿¹ Minkowski plane ⋮ Energy Estimates and Cavity Interaction for a Critical-Exponent Cavitation Model

Cites Work

• A sharp isoperimetric inequality in the plane
• Rearrangements and convexity of level sets in PDE
• Area minimizing sets subject to a volume constraint in a convex set
• A problem in the theory of subordination
• The sharp quantitative isoperimetric inequality
• Bonnesen-Style Isoperimetric Inequalities
• The isoperimetric inequality
• Stability in the Isoperimetric Problem for Convex or Nearly Spherical Domains in R n
• Radial Functions of Convex and Star-Shaped Bodies
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A sharp isoperimetric inequality in the plane involving Hausdorff distance