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

Christine Laurent-Thiébaut ()
Additional contact information
Christine Laurent-Thiébaut: Université Joseph Fourier, Institut Fourier

A chapter in Holomorphic Function Theory in Several Variables, 2011, pp 195-209 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2011
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-85729-030-4_8

Ordering information: This item can be ordered from
http://www.springer.com/9780857290304

DOI: 10.1007/978-0-85729-030-4_8

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().