Exhaustion functions and Stein neighborhoods for smooth pseudoconvex domains
- 1 September 1975
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 72 (9) , 3279-3280
- https://doi.org/10.1073/pnas.72.9.3279
Abstract
A strictly plurisubharmonic exhaustion function with negative values is constructed for arbitrary relatively compact pseudoconvex domains with smooth boundary in a Stein manifold. It is applied to verify the Serre conjecture in a special case. A sufficient condition is given that guarantees the existence of a neighborhood-basis of Stein domains for certain bounded pseudoconvex domains on a Stein manifold.Keywords
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