Cartan uniqueness theorem on nonopen sets (Q2086429)

Cartan's uniqueness theorem does not hold in general when a bounded domain in \(\mathbb{C}^n\) is replaced by a real subvariety and holomorphic mappings replaced by CR mappings. It is interesting to establish a CR analogue of this theorem. The authors deal with a version of Cartan's theorem. They generalize two conditions on the mapping in the theorem, one is that the derivative is the identity at a point, and the other is that the mapping takes a bounded domain to itself. With also the contracting disc hull condition, the paper shows that the infinitesimal automorphism is simply the zero vector field.