Real-analytic submanifolds which are local uniqueness sets for holomorphic functions of $\textbf {C}^{3}$

Abstract:

The following problem is considered. Given a real-analytic two-dimensional submanifold, $M$, of complex Euclidean three-space, are ambient holomorphic functions determined by their values on $M?$ For a large class of submanifolds a necessary and sufficient condition is found for $M$ to be a local uniqueness set for holomorphic functions on complex three-space. Finally, the general problem is shown to be related to two-dimensional Nevanlinna theory.