×

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 \(f\).

MSC:
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