On the quantitative isoperimetric inequality in the plane with the barycentric distance

Chiara Bianchini, Gisella Croce, Antoine Henrot

In this paper we study the following quantitative isoperimetric inequality in the plane: ${\lambda }_0^2(\Omega )\le C\delta (\Omega )$ where $\delta$ is the isoperimetric deficit and ${\lambda }_0$ is the barycentric…