Boundary problem in compactifications of \(\mathbb{C}^n\) (Q2708185)

Let \(\gamma\) be a closed and compact 1-chain of class \(C^2\) in \(\mathbb{C}^n\), possibly with a negligible singular subset, and \((X,Z)\) a compactification of \(\mathbb{C}^n\).NEWLINENEWLINENEWLINEThe author gives suffficient conditions for \((X,Z)\) such that the following two statements are equivalent: NEWLINENEWLINENEWLINE(i) \(\gamma\) is the boundary of a holomorphic 1-chain \(S\) of finite mass of \(\mathbb{C}^n\setminus\gamma\); NEWLINENEWLINENEWLINE(ii)\(\gamma\) is the boundary of a holomorphic 1-chain \(S_1\) of finite mass of \(X\setminus\gamma\). The paper is well written and contains several interesting examples.