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@article{faucris.282430048,
abstract = {The object of the paper is to find complete systems of inequalities relating the perimeter P, the area vertical bar.vertical bar and the Cheeger constant h of planar sets. To do so, we study the so-called Blaschke-Santalo diagram of the triplet (P, h, vertical bar.vertical bar) for different classes of domains: simply connected sets, convex sets and convex polygons with at most N sides. We completely determine the diagram in the latter cases except for the class of convex N-gons when N >= 5 is odd: therein, we show that the boundary of the diagram is given by the graphs of two continuous and strictly increasing functions. An explicit formula for the lower one and a numerical method to obtain the upper one is provided. At last, some applications of the results are presented.},
author = {Ftouhi, Ilias},
doi = {10.1142/S0219199722500547},
faupublication = {yes},
journal = {Communications in Contemporary Mathematics},
note = {CRIS-Team WoS Importer:2022-09-30},
peerreviewed = {Yes},
title = {{Complete} systems of inequalities relating the perimeter, the area and the {Cheeger} constant of planar domains},
year = {2022}
}