Characterizations of boundaries of holomorphic 1-chains within ℂ ̂ × ℂ̂ and ℂ ̂ × ℂ̂

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Abstract

By way of a particular Cauchy-type integral, we characterize the closed rectifiable 1-currents γ, with support contained in ℂ 2 and satisfying condition A 1, that bound holomorphic 1-chains within ℂ̂× ℂ̂ . Also, we derive characterizations for the boundaries of holomorphic 1-chains within ℂ̂× ℂ̂, which yield examples of characterizations within a non-compact, non-Stein space. Additionally, we illustrate a connection between some of these characterizations and the Cauchy integral characterization of boundary values of meromorphic and holomorphic functions over a domain in ℂ.

Original languageEnglish (US)
Pages (from-to)1159-1170
Number of pages12
JournalJournal of Geometric Analysis
Volume18
Issue number4
DOIs
StatePublished - Oct 1 2008

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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