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@article{faucris.279551397,
abstract = {In this short note, we prove that for every bounded, planar and convex set Ω, one has (equation presented) where λ1, T , r and j j are the first Dirichlet eigenvalue, the torsion, the inradius and the volume. The inequality is sharp as the equality asymptotically holds for any family of thin collapsing rectangles. As a byproduct, we obtain the following bound for planar convex sets (equation presented) which improves Polyá's inequality λ1(Ω)T (Ω) jΩj Ç 1 and is slightly better than the one provided in [3]. The novel ingredient of the proof is the sharp inequality (equation presented) recently proved in [8].},
author = {Ftouhi, Ilias},
doi = {10.5802/crmath.292},
faupublication = {yes},
journal = {Comptes Rendus Mathematique},
note = {CRIS-Team Scopus Importer:2022-08-05},
pages = {241-246},
peerreviewed = {Yes},
title = {{On} a {Pólya}'s inequality for planar convex sets},
volume = {360},
year = {2022}
}