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dc.contributor.authorZAITSEV, DMITRI
dc.date.accessioned2009-08-31T15:09:35Z
dc.date.available2009-08-31T15:09:35Z
dc.date.issued2003
dc.date.submitted2003en
dc.identifier.citationMeylan, Francine; Mir, Nordine; Zaitsev, Dmitri 'Holomorphic extension of smooth CR-mappings between real-analytic and real-algebraic CR-manifolds' in Asian Journal of Mathematics, 7, (4), 2003, pp 493 - 509en
dc.identifier.otherY
dc.identifier.otherYen
dc.identifier.urihttp://hdl.handle.net/2262/31980
dc.descriptionPUBLISHEDen
dc.description.abstractThe classical Schwarz reflection principle states that a continuous map f between real-analytic curves M and M? in C that locally extends holomorphically to one side of M, extends also holomorphically to a neighborhood of M in C. It is well-known that the higher-dimensional analog of this statement for maps f : M ? M? between real-analytic CR-submanifolds M ? CN andM? ? CN? does not hold without additional assumptions (unless M andM? are totally real). In this paper, we assume that f is C?-smooth and that the target M? is real-algebraic, i.e. contained in a real-algebraic subset of the same dimension. If f is known to be locally holomorphically extendible to one side of M (when M is a hypersurface) or to a wedge with edge M (when M is a generic submanifold of higher codimension), then f automatically satisfies the tangential Cauchy- Riemann equations, i.e. it is CR. On the other hand, if M is minimal, any CR-map f : M ? M? locally extends holomorphically to a wedge with edge M by Tumanov?s theorem [Tu88] and hence, in that case, the extension assumption can be replaced by assuming f to be CR.en
dc.description.sponsorshipThe first author was partially supported by Swiss NSF Grant 2100-063464.00/1.en
dc.format.extent493en
dc.format.extent509en
dc.format.extent299319 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoenen
dc.publisherInternational Pressen
dc.relation.ispartofseriesAsian Journal of Mathematicsen
dc.relation.ispartofseries7en
dc.relation.ispartofseries4en
dc.rightsYen
dc.subjectPure & Applied Mathematicsen
dc.titleHolomorphic extension of smooth CR-mappings between real-analytic and real-algebraic CR-manifoldsen
dc.typeJournal Articleen
dc.type.supercollectionscholarly_publicationsen
dc.type.supercollectionrefereed_publicationsen
dc.identifier.peoplefinderurlhttp://people.tcd.ie/zaitsevd
dc.identifier.rssinternalid37980


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