On a Pólya’s inequality for planar convex sets
In this short note, we prove that for every bounded, planar and convex set $\Omega $, one has \[ \frac{\lambda _1(\Omega )T(\Omega )}{|\Omega |}\le \frac{\pi ^2}{12}\cdot \left(1+\sqrt{\pi }\frac{r(\Omega )}{\sqrt{|\Omega |}}\right)^2, \] where $\lambda _1$, $T$, $r$ and $|{\,\cdot \,}|$ are the fir...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2022-03-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.292/ |