Alexandrov, Serrin, Weinberger, Reilly: Simmetry and Stability by Integral Identities

Abstract

The distinguished names in the title have to do with different proofs of the celebrated Soap Bubble Theorem and of radial symmetry in certain overdetermined boundary value problems. We shall give an overeview of those results and indicate some of their ramifications. We will also show how more recent proofs uncover the path to some stability results for the relevant problems.

Keywords

• Serrin's overdetermined problem
• Alexandrov Soap Bubble Theorem
• torsional rigidity
• constant mean curvature
• integral identities
• quadrature identities
• stability
• quantitative estimates