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• W2950561238 abstract "We study the existence of topologically closed complex curves normalized by bordered Riemann surfaces in complex spaces. Our main result is that such curves abound in any noncompact complex space admitting an exhaustion function whose Levi form has at least two positive eigenvalues at every point outside a compact set, and this condition is essential. The proof involves a lifting method for the boundary of the curve and a newly developed technique of gluing holomorphic sprays over Cartan pairs in Stein manifolds whose value lie in a complex space, with control up to the boundary of the domains. (The latter technique is also exploited in the subsequent papers math.CV/0607185 and math.CV/0609706.) We also prove that any compact complex curve with C^2 boundary in a complex space admits a basis of open Stein neighborhoods. In particular, an embedded disc of class C^2 with holomorphic interior in a complex manifold admits a basis of open polydisc neighborhoods." @default.
• W2950561238 created "2019-06-27" @default.
• W2950561238 creator A5034701861 @default.
• W2950561238 creator A5043857437 @default.
• W2950561238 date "2006-04-05" @default.
• W2950561238 modified "2023-09-27" @default.
• W2950561238 title "Holomorphic curves in complex spaces" @default.
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• W2950561238 hasPublicationYear "2006" @default.
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