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VIII Characterisation of removable singularities of CR functions on a strictly pseudoconvex boundary

  • Christine Laurent-Thiébaut
Chapter

Abstract

We start this chapter by giving various characterisations of the compact sets K in the boundary of a strictly pseudoconvex domain D in a Stein manifold of dimension n which have the following property: any continuous CR function on \(\partial D\backslash K\) can be extended holomorphically to the whole of D. We will obtain a geometric characterisation of such sets for n = 2 and a cohomological characterisation of such sets for n ⩾ 3. Amongst other things, we prove that the suffcient cohomological condition given in Theorem 5.1 of Chapter V is necessary if the ambient manifold is Stein and the domain D is assumed strictly pseudoconvex. We end the section with a geometric characterisation of the compact sets K such that any continuous CR function defined on \(\partial D\backslash K\)which is orthogonal to the set of \(\overline{\partial}\) -closed (n; n−1)-forms whose support does not meet K can be extended holomorphically to the whole of D. When K is empty this condition is just the hypothesis of Theorem 3.2 of Chapter IV.

Keywords

Holomorphic Function Erential Form Pseudoconvex Domain Geometric Characterisation Removable Singularity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Institut FourierUniversité Joseph FourierSaint-Martin d’Hères CedexFrance

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