Let M be a manifold of X = ℂn, A a small analytic disc attached to M, z0 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 z0 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.
Analytic discs and extension of CR functions
ZAMPIERI, GIUSEPPE;BARACCO, LUCA
2001
Abstract
Let M be a manifold of X = ℂn, A a small analytic disc attached to M, z0 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 z0 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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