An existence result for a quantitative isoperimetric inequality in ${\mathbb{R}}^3$ involving the Hausdorff asymmetry

Silvio Bove, Gisella Croce, Giovanni Pisante

We study the existence of an optimizer for a quantitative isoperimetric ratio ${\mathcal{Q}}_{\ast }$ in ${\mathbb{R}}^3$ involving the Hausdorff asymmetry. We prove that ${\mathcal{Q}}_{\ast }$ att…