Ilaria Fragalà

Proof of the local version of the P\'olya--Szeg\"o conjecture for the torsional rigidity of polygons

We prove the local version of the P\'olya--Szeg\"o 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 proportional triangula...