Real-Analytic Submanifolds Which are Local Uniqueness Sets for Holomorphic Functions of C 3
Copyright policy )Real-Analytic Submanifolds Which are Local Uniqueness Sets for Holomorphic Functions of C 3
The following problem is considered. Given a real-analytic two-dimensional submanifold, M M , of complex Euclidean three-space, are ambient holomorphic functions determined by their values on M ? M? For a large class of submanifolds a necessary and sufficient condition is found for M 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.
Real-analytic manifolds, real-analytic spaces, uniqueness set for germs of holomorphic functions, Analytic subsets and submanifolds, Real submanifolds in complex manifolds, real-analytic real 2-dimensional surface, Power series rings
Real-analytic manifolds, real-analytic spaces, uniqueness set for germs of holomorphic functions, Analytic subsets and submanifolds, Real submanifolds in complex manifolds, real-analytic real 2-dimensional surface, Power series rings
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