Analytic continuation of holomorphic mappings

Ayed, Besma; Ourimi, Nabil

doi:10.1016/j.crma.2009.07.001

Cited by 6 publications

(3 citation statements)

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“…Our main theorem is the following: By a smooth real-algebraic hypersurface we mean a real hypersurface in C n globally defined by a polynomial equation P (z,z) = 0. A similar result was proved in [1] for holomorphic mappings. Note that we do not require pseudoconvexity of M or M ′ .…”

Section: Introduction and Main Resultssupporting

confidence: 56%

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On Boundary Regularity of Holomorphic Correspondences

Ourimi¹

2012

Journal of the Korean Mathematical Society

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Abstract. Let D be an arbitrary domain in C n , n > 1, and M ⊂ ∂D be an open piece of the boundary. Suppose that M is connected and ∂D is smooth real-analytic of finite type (in the sense of D'Angelo) in a neighborhood ofM . Let f : D → C n be a holomorphic correspondence such that the cluster set cl f (M ) is contained in a smooth closed real-algebraic hypersurface M ′ in C n of finite type. It is shown that if f extends continuously to some open peace of M , then f extends as a holomorphic correspondence across M . As an application, we prove that any proper holomorphic correspondence from a bounded domain D in C n with smooth real-analytic boundary onto a bounded domain D ′ in C n with smooth real-algebraic boundary extends as a holomorphic correspondence to a neighborhood ofD.

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Section: Introduction and Main Resultssupporting

confidence: 56%

“…Assume thatM h ̸ = M h and let q ∈ ∂M h =M h \M h . We follow the idea in [22], used also in [1]. Since M is globally minimal, there exists a CR-curve γ (i.e., the tangent vector to γ at any point is contained in the complex tangent to M ) passing through q and entering M h .…”

Section: Proof Of Theoremmentioning

confidence: 99%