THE STRONG OKA'S LEMMA, BOUNDED PLURISUBHARMONIC FUNCTIONS AND THE 3-NEUMANN PROBLEM

摘要

The classical Oka's Lemma states that if fl is a pseudoconvex domain in C", n > 2, then -logS is plurisubharmouic where S is some distance function to the boundary. Let M be a complex hermitian manifold with the metric form u>. Let Q be relatively compact pseudoconvex domain in M. We say that a distance function 5 to the boundary bQ satisfies the strong Oka condition if it can be extended from a neighborhood of bQ to f2 such that 5 satisfies for some constant CQ > 0.