Analytic Discs Attached to Half Spaces of $Bbb C^n$ and Extension of Holomorphic Functions

摘要

Let$M$bearealhypersurfaceof$C^n$,$M^+$aclosedhalfspacewithboundary$M$,$z_o$apointof$M$.Weprovethattheexistenceofadisc$A$tangentto$M$at$z_o$,attachedto$M^+$butnotto$M$(i.e.$partialAsubsetM^+$but$partialA otsubsetM$),entailsextensionofholomorphicfunctionsfromtheinteriorof${M^+}$toafullneighborhoodof$z_o$.Thisresultcoversaresultincite{9},wherethedisc$A$isassumedtolieononeside$M^+$of$M$.Thebasicidea,whichunderliestothewholepaper,isduetoA.Tumanov[8]andconsistsinattachingdiscstomanifoldswithboundary.Further,holomorphicextendabilitybytheaidoftangentdiscsattachedto$M$andof"defect0"isaparticularcaseofageneraltheoremof"wedgeextendibility"ofCR--functionsbyA.Tumanov.