A continuation theorem for meromorphic maps (Q5947132)

Let \(X,Y\) be connected complex manifolds (countable at infinity). A connected locally irreducible analytic set \(Z\subset Y\times X\) is a meromorphic function on \(Y\) (in the sense of Remmert) if there exists an analytic set \(\Sigma\subset Y\) such that \(Z\cap((Y\setminus\Sigma)\times X)\) coincides with the graph of a holomorphic mapping \(f:Y\setminus\Sigma\rightarrow X\), and the natural projection \(Z\rightarrow Y\) is proper. The main result of the paper is an extension theorem which says that if \(M\) is a connected \((n+1)\)-dimensional Stein manifold and \(K\subset M\) is a compact set such that \(M\setminus K\) is connected, then any meromorphic function on \(M\setminus K\) of rank \(\leq n\) extends meromorphically to the whole \(M\).