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Holomorphic curves in complex spaces

By Franc Forstnerič


Abstract. We study the existence of closed complex curves normalized by bordered Riemann surfaces in complex spaces. Our main result is that such curves abound in any non compact 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. We also construct a Stein neighborhood basis of any compact complex curve with C 2 boundary in a complex space. 1

Year: 2006
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