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Analytic Discs and Extension of CR Functions

Published online by Cambridge University Press:  04 December 2007

Luca Baracco  and
Giuseppe Zampieri
Luca Baracco
Affiliation:
Universita di Padova, Dipartimento De Matematica, Via Belzoni 7, 35131 Padova, Italy
Giuseppe Zampieri
Affiliation:
Universita di Padova, Dipartimento De Matematica, Via Belzoni 7, 35131 Padova, Italy. E-mail: zampieri@math.unipd.it
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Abstract

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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.

Keywords

CR functionanalytic discs
Type
Research Article
Information
Compositio Mathematica , Volume 127 , Issue 3 , July 2001 , pp. 289 - 295
Copyright
© 2001 Kluwer Academic Publishers