A quantitative reverse Faber-Krahn inequality for the first Robin eigenvalue with negative boundary parameter

The aim of this paper is to prove a quantitative form reverse Faber-Krahn type inequality for the first Robin Laplacian eigenvalue λ β with negative boundary parameter among convex sets prescribed perimeter. In that framework, ball only maximizer and distance from optimal set considered in terms Hausdorff distance. key point our stategy Steklov-type problem related original problem.