PSEUDOCONCAVE DECOMPOSITIONS IN COMPLEX MANIFOLDS
Zbigniew Slodkowski
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Abstract
We prove that the core of a complex manifold X is the union of pairwise disjoint pseudoconcave sets on which all uniformly bounded continuous plurisubharmonic functions on X are constant. Similarly, the minimal kernel of a weakly complete complex manifold decomposes into the union of compact pseudoconcave sets on which all continuous plurisub-harmonic functions are constant. Versions of these results for standard smoothness classes are obtained. Analogous facts are discussed in the context of Richberg's regularization of continuous strongly plurisubharmonic functions.
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