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Analytic Discs and Extension of CR Functions

Research paper by Luca Baracco, Giuseppe Zampieri

Indexed on: 01 Jul '01Published on: 01 Jul '01Published in: Compositio Mathematica



Abstract

Let M be a manifold of X = Cn, 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.