Optimal sets for the quantitative isoperimetric inequality in the plane with the barycentric distance

Gisella Croce, Antoine Henrot

In a recent paper, C. Gambicchia and A. Pratelli proved a quantitative isoperimetric inequality involving the isoperimetric deficit $\hat{I}´(K)$ and the barycentric distance $\hat{I}{»}_0(K)$ f…