Holomorphic extension from a convex hypersurface

TL;DR

This paper establishes conditions under which a real analytic function defined on the boundary of a convex domain in complex space can be holomorphically extended into the domain, based on extension along special discs.

Contribution

It demonstrates that separate holomorphic extension along stationary discs implies full holomorphic extension for functions on convex hypersurfaces.

Findings

Holomorphic extension follows from extension along stationary discs

Extension is valid for real analytic functions on convex boundaries

Provides a general criterion for holomorphic extension in complex analysis

Abstract

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 $D\subset\subset \C^n$. We show that this follows from the hypothesis of separate holomorphic extension along stationary/extremal discs.