Parametric argument principle and its applications to CR functions and manifolds

Abstract

A version of the argument principle is established for varieties of holomorphic mappings from the unit disc to ${\mathbb{C}}^n,$ parametrized by points of real manifolds. Applications to characterization of CR functions and estimating CR dimensions of real submanifolds in ${\mathbb{C}}^n$ are given.

Accepted in Advances in Mathematics. arXiv admin note: text overlap with arXiv:0704.2871

References in corpus (2)

• Extremal discs and the holomorphic extension from convex hypersurfaces
• Complex dimensions of real manifolds, attached analytic discs and parametric argument principle