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International Mathematics Research Notices 1, 1997 (1997) 21-56

On removable singularities for CR functions in higher codimension

Joel Merker 1

(1996)

We establish the holomorphic wedge extendability of CR functions, defined on an everywhere locally minimal generic submanifold M of C^n and having singularities contained in a submanifold N of codimension 1, 2 or 3, assuming some transversality conditions about the relative disposition of N with respect to the complex tangent bundle to M. The statements hold in arbitrary codimension and are obtained by applying the theory of normal deformations of analytic discs, due to A.E. Tumanov in 1994 and also the FBI propagation of singularities phenomenon enjoyed by CR functions, due to J.-M. Trepreau in 1990. Related results in the hypersurface case were obtained simultaneously by B. Joricke in 1992-96 and by E. Porten in his thesis (1996).

1:	Laboratoire d'Analyse, Topologie, Probabilités (LATP)
	CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III

Subject

:

Mathematics/Differential Geometry

Keyword(s): removable singularities – CR functions – minimality in the sense of J.-M. Trepreau and A.E. Tumanov – analytic discs – wedges – holomorphic extension

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From: Joel Merker <>

Submitted on: Saturday, 27 November 2004 15:16:31

Updated on: Sunday, 28 November 2004 09:32:06