Extension of Holomorphic Functions From One Side of a Hypersurface

We give a new proof of former results by G. Zampieri and the author on extension of holomorphic functions from one side Ω of a real hypersurface M of ℂn in the presence of an analytic disc tangent to M, attached to Ω but not to M. Our method enables us to weaken the regularity assumptions both for the hypersurface and the disc.

Analytic discs in the polynomial hull of a disc fibration over the sphere

It is shown that for each point P in the interior of the polynomial hull of a disc fibration X over the unit sphere ∂n there exists an H∞ analytic disc with boundary in X and passing through p.