Exhaustion functions and Stein neighborhoods for smooth pseudoconvex domains.
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.
Princeton University, Department of Mathematics, Fine Hall, Box 37, Princeton, New Jersey 08540.
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