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@article{faucris.323034409,
abstract = {We are interested in finding sharp bounds for the Cheeger constant h via different geometrical quantities, namely the area |€ ¢|, the perimeter P, the inradius r, the circumradius R, the minimal width w and the diameter d. We provide new sharp inequalities between these quantities for planar convex bodies and enounce new conjectures based on numerical simulations. In particular, we completely solve the Blaschke-Santaló diagrams describing all the possible inequalities involving the triplets (P, h, r), (d, h, r) and (R, h, r) and describe some parts of the boundaries of the diagrams of the triplets (w, h, d), (w, h, R), (w, h, P), (w, h, |€ ¢|), (R, h, d) and (w, h, r).},
author = {Ftouhi, Ilias and Masiello, Alba Lia and Paoli, Gloria},
doi = {10.1051/cocv/2024015},
faupublication = {yes},
journal = {Esaim-Control Optimisation and Calculus of Variations},
keywords = {Blaschke-Santaló diagrams; Cheeger constant; Convex sets; Sharp inequalities},
note = {CRIS-Team Scopus Importer:2024-05-31},
peerreviewed = {Yes},
title = {{Sharp} inequalities involving the {Cheeger} constant of planar convex sets},
volume = {30},
year = {2024}
}