Holomorphic Chains and Extendability of Holomorphic Mappings

Pierre Dolbeault and Julian Ławrynowicz
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Pierre Dolbeault: Université Pierre et Marie Curie, Mathématiques, L.A. 213 du C.N.R.S.
Julian Ławrynowicz: Polish Academy of Sciences, Institute of Mathematics

A chapter in Deformations of Mathematical Structures, 1989, pp 191-204 from Springer

Abstract: Abstract The authors introduce a Dirichlet integral-type biholo-morphic-invariant pseudodistance connected with bordered holomorphic chains of dimension one whose regular part is treated as a Riemann surface. The condition for a complex manifold that the pseudodistance on it is a distance defines a class of hyperbolic-like manifolds which have an important property of extendability of holomorphic mappings, analogous to the hyperbolic manifolds, Stein spaces, and complex spaces with a Stein covering.

Keywords: Riemann Surface; Holomorphic Mapping; Complex Space; Complex Manifold; Hyperbolic Manifold (search for similar items in EconPapers)
Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-2643-1_18

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DOI: 10.1007/978-94-009-2643-1_18

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