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We give a new proof of former results by $\text{G}$. Zampieri and the author on extension of holomorphic functions from one side $\Omega$ of a real hypersurface $M$ of ${{\mathbb{C}}^{n}}$ in the presence of an analytic disc tangent to $M$, attached to $\bar{\Omega }$ but not to $M$. Our method enables us to weaken the regularity assumptions both for the hypersurface and the disc.

Let M be a manifold of X = $\Bbb C$n, A a small analytic disc attached to M, zo a point of ∂A where A is tangent to M, z1 another point of ∂A where M extends to a germ of manifold M1 with boundary M. We prove that CR functions on M which extend to M1 at z1 also extend at zo to a new manifold M2. The directions M1 and M2 point to, are related by a sort of connection associated to A which is dual to the connection obtained by attaching ‘partial analytic lifts’ of A to the co-normal bundle to M in X.

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Extension of Holomorphic Functions From One Side of a Hypersurface

Analytic Discs and Extension of CR Functions

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2 results

Extension of Holomorphic Functions From One Side of a Hypersurface

Analytic Discs and Extension of CR Functions