A sharp lower bound on the polygonal isoperimetric deficit

DOI10.1090/proc/12947zbMath1345.52005arXiv1502.05978OpenAlexW2963431466MaRDI QIDQ2802128

Emanuel Indrei

Publication date: 25 April 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.05978

zbMATH Keywords

varianceradiipolygonsisoperimetric deficitconvex \(n\)-gonbarycentric angles

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) Convex sets in (2) dimensions (including convex curves) (52A10) Length, area and volume in real or complex geometry (51M25) Inequalities and extremum problems in real or complex geometry (51M16)

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Cites Work

• A Faber-Krahn inequality for the Cheeger constant of \(N\)-gons
• A sharp quantitative version of Hales' isoperimetric honeycomb theorem
• A mass transportation approach to quantitative isoperimetric inequalities
• The honeycomb conjecture
• A sharp stability result for the relative isoperimetric inequality inside convex cones
• On the stability of the polygonal isoperimetric inequality
• The sharp quantitative isoperimetric inequality
• A note on the stability of the Cheeger constant of $N$-gons
• Perpendicular Polygons