Exhaustion functions and Stein neighborhoods for smooth pseudoconvex domains

AUTOR(ES)

Diederich, Klas

RESUMO

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.

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