dc.contributor.author | ZAITSEV, DMITRI | |
dc.date.accessioned | 2009-08-31T15:09:35Z | |
dc.date.available | 2009-08-31T15:09:35Z | |
dc.date.issued | 2003 | |
dc.date.submitted | 2003 | en |
dc.identifier.citation | Meylan, 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 - 509 | en |
dc.identifier.other | Y | |
dc.identifier.other | Y | en |
dc.identifier.uri | http://hdl.handle.net/2262/31980 | |
dc.description | PUBLISHED | en |
dc.description.abstract | The 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.sponsorship | The first author was partially supported by Swiss NSF Grant 2100-063464.00/1. | en |
dc.format.extent | 493 | en |
dc.format.extent | 509 | en |
dc.format.extent | 299319 bytes | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | en |
dc.publisher | International Press | en |
dc.relation.ispartofseries | Asian Journal of Mathematics | en |
dc.relation.ispartofseries | 7 | en |
dc.relation.ispartofseries | 4 | en |
dc.rights | Y | en |
dc.subject | Pure & Applied Mathematics | en |
dc.title | Holomorphic extension of smooth CR-mappings between real-analytic and real-algebraic CR-manifolds | en |
dc.type | Journal Article | en |
dc.type.supercollection | scholarly_publications | en |
dc.type.supercollection | refereed_publications | en |
dc.identifier.peoplefinderurl | http://people.tcd.ie/zaitsevd | |
dc.identifier.rssinternalid | 37980 | |