Holomorphic extension from a convex hypersurface

We discuss a general result of holomorphic extension of a real analytic function $f$ defined on the boundary $\partial D$ of a real analytic strictly convex subset $D \subset \subset \mathbb{C}^n$. We show that this follows from the hypothesis of separate holomorphic extension along stationary/extremal discs.

Keywords

analytic discs, continuity principle, separate analiticity

2010 Mathematics Subject Classification

32D10, 32N15, 32V10

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Published 18 March 2016