zbMATH — the first resource for mathematics

A generalization of Kerner’s theorem on proper maps. (English. Russian original) Zbl 1214.32005
From the text: We prove a generalization of H. Kerner’s theorem [Arch. Math. 11, 44–49 (1960; Zbl 0095.06303)] about the extension of proper maps: Theorem 2. Let \(D_1\) be a subdomain of a Stein manifold, \(\widehat D_1\) its envelope of holomorphy, and \(D_2\) a complex manifold of the same dimension \(n\geq 2\). Suppose that there is a proper holomorphic map \(f:D_1\to D_2\). Then there exists a Stein space \(\widehat D_2 \supset D_2\) that is the envelope of holomorphy of \(D_2\), and there exists a proper holomorphic map \(\widehat f:\widehat D_1\to \widehat D_2\) extending \(f\).

32H35 Proper holomorphic mappings, finiteness theorems
32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables
32D10 Envelopes of holomorphy
32E10 Stein spaces
PDF BibTeX Cite
Full Text: DOI