On the stability for Alexandrov's Soap Bubble theorem

  title={On the stability for Alexandrov's Soap Bubble theorem},
  author={Rolando Magnanini and Giorgio Poggesi},
Alexandrov's Soap Bubble theorem dates back to $1958$ and states that a compact embedded hypersurface in $\mathbb{R}^N$ with constant mean curvature must be a sphere. For its proof, A.D. Alexandrov invented his reflection priciple. In $1982$, R. Reilly gave an alternative proof, based on integral identities and inequalities, connected with the torsional rigidity of a bar. In this article we study the stability of the spherical symmetry: the question is how much a hypersurface is near to a… CONTINUE READING
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