Geometric properties of optimizers for the maximum gradient of the torsion function

Krzysztof Burdzy, Ilias Ftouhi, Phanuel Mariano

Consider $J(\hat{I}\text{c◯}):=\Vert \nabla u_{\hat{I}}\text{c◯}{\Vert }_{\infty }/\sqrt{|\hat{I}\text{c◯}|}$ and $J_P(\hat{I}\text{c◯}):=\Vert \nabla u_{\hat{I}}\text{c◯}{\Vert }_{\infty }/P(\hat{I}\text{c◯})$, where $\hat{I}\text{c◯}$ is a planar convex domain, $u_{\hat{I}}\text{c◯}$ is the torsion function, $P(\hat{I}\text{c◯})$…