Rigidity in CR geometry: The Schoen-Webster theorem (Q1023413)

Suppose \(M\) is a connected strongly pseudoconvex CR-manifold whose automorphism group acts nonproperly. \textit{R. Schoen} [Geom. Funct. Anal. 5, No. 2, 464--481 (1995; Zbl 0835.53015)] proved that \(M\) is then CR-equivalent to a sphere or the Heisenberg group. This paper presents a survey on the background and results related to this, and another proof when \(M\) is compact.