Vigna Suria, Giuseppe q-pseudoconvex and q-complete domains. (English) Zbl 0566.32012 Compos. Math. 53, 105-111 (1984). Main result: If D is a domain with \(C^ 2\) boundary in a Stein manifold M and D has q-pseudoconvex boundary, then D is q-complete. The proof uses a reduction (by embedding and tubular neighbourhood) to the case \(M={\mathbb{C}}^ N\). Reviewer: E.Ballico Cited in 6 Documents MSC: 32F10 \(q\)-convexity, \(q\)-concavity 32U05 Plurisubharmonic functions and generalizations 32E10 Stein spaces Keywords:q-complete domain; plurisubharmonic function; Stein manifold; pseudoconvex boundary PDFBibTeX XMLCite \textit{G. Vigna Suria}, Compos. Math. 53, 105--111 (1984; Zbl 0566.32012) Full Text: Numdam EuDML References: [1] K. Diederich and J.E. Fornaess : Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions . Inv. Math. 39 (1977) 129-141. · Zbl 0353.32025 [2] M.G. Eastwood and G. Vigna Suria : Cohomologically complete and pseudoconvex domains . Comm. Math. Helv. 55 (1980) 413-426. · Zbl 0464.32010 [3] H. Grauert : On Levi’s problem and the embedding of real analytic manifolds . Ann. Math. 68 (1958) 460-472. · Zbl 0108.07804 [4] L. Hormander : An introduction to complex analysis in several variables . Princeton N.J. Van Nostrand (1966). · Zbl 0138.06203 [5] R. Narasimhan : The Levi problem for complex spaces . Math. Ann. 142 (1961) 355-365. · Zbl 0106.28603 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.