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Analytic Discs and Extension of CR Functions

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Compositio Mathematica

Abstract

Let M be a manifold of X = Cn, A a small analytic disc attached to M, z o a point of ∂A where A is tangent to M, z 1 another point of ∂A where M extends to a germ of manifold M 1 with boundary M. We prove that CR functions on M which extend to M 1 at z 1 also extend at z o to a new manifold M 2. The directions M 1 and M 2 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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Authors and Affiliations

  1. Dipartimento De Matematica, Universita di Padova, Via Belzoni 7, 35131, Padova, Italy

    Luca Baracco

  2. Universita di Padova, Dipartimento De Matematica, Via Belzoni 7, 35131, Padova, Italy

    Giuseppe Zampieri

Authors
  1. Luca Baracco
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  2. Giuseppe Zampieri
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Baracco, L., Zampieri, G. Analytic Discs and Extension of CR Functions. Compositio Mathematica 127, 289–295 (2001). https://doi.org/10.1023/A:1017581000515

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  • DOI: https://doi.org/10.1023/A:1017581000515

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