On the stability for Alexandrov’s Soap Bubble theorem

Alexandrov’s Soap Bubble Theorem dates back to 1958 and states that a compact embedded hypersurface in ℝN with constant mean curvature must be a sphere. For its proof, A. D. Alexandrov invented his reflection principle. In 1977, R. Reilly gave an alternative proof, based on integral identities and inequalities, connected with the torsional rigidity of a bar.