Author

Beniamin Bogosel

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Preprint Aug 2026

Isoperimetric problems related to extremal diameter graphs in 3D: theoretical and numerical aspects

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 dimensions. For a fixed diameter graph, these problems lead to nonconvex constrained optimization of the vertex coordinates. We first prove that a co...

Beniamin Bogosel · 1 citation

Preprint Sep 2026

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...

Beniamin Bogosel, D. Bucur, Ilaria Fragalà · 0 citations