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math.SP2026
Proof of the local version of the Pólya--Szegö conjecture for the torsional rigidity of polygons
Beniamin Bogosel, Dorin Bucur, Ilaria Fragalà
We prove the local version of the Pólya--Szegö conjecture for the torsional rigidity of polygons: for every \(n\geq5\), the regular -gon is a strict local maximizer of torsional…
math.OC2026
Symmetry breaking in the polygonal Szegö-Weinberger inequality as : the longest shortest-fence quadrilateral
Beniamin Bogosel, Dorin Bucur, Ilaria Fragalà
We consider Pólya's problem of finding, among convex sets of prescribed area, the one with the longest shortest fence, in the polygonal setting, namely when the class of competitor…
math.OC2026
Isoperimetric problems related to extremal diameter graphs in 3D: theoretical and numerical aspects
Beniamin Bogosel
We study optimization problems for separable functionals of the Euclidean or spherical lengths of dual edge pairs in finite extremal unit-diameter configurations in three dimension…