Symmetry breaking in the polygonal Szegö-Weinberger inequality as $p\to 1^{+}$: 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…