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Proof of the local version of the Pólya--Szegö conjecture for the torsional rigidity of polygons
We prove the local version of the Pólya--Szegö conjecture for the torsional rigidity of polygons: for every \(n\geq5\), the regular $n$-gon is a strict local maximizer of torsional rigidity among convex $n$-gons of prescribed area. Our proof is entirely analytic. It builds on a locally stable prop
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