Ftouhi I (2022)
Publication Type: Journal article
Publication year: 2022
Book Volume: 360
Pages Range: 241-246
DOI: 10.5802/crmath.292
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].
APA:
Ftouhi, I. (2022). On a Pólya's inequality for planar convex sets. Comptes Rendus Mathematique, 360, 241-246. https://dx.doi.org/10.5802/crmath.292
MLA:
Ftouhi, Ilias. "On a Pólya's inequality for planar convex sets." Comptes Rendus Mathematique 360 (2022): 241-246.
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