2006/08/10 by Ebenfelt, Peter, Rothschild, Linda P.
#32H35 #32V40 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.math/0608272
We consider a smooth CR mapping f from a real-analytic generic submanifold M in \bCN into \bCN. For M of finite type and essentially finite at a point p∈ M, and f formally finite at p, we give a necessary and sufficient condition for f to extend as a holomorphic mapping in some neighborhood of p. In a similar vein, we consider a formal holomorphic mapping H and give a necessary and sufficient condition for H to be convergent.