Relative types and extremal problems for plurisubharmonic functions

Details Relative types and extremal problems for plurisubharmonic functions Relative types and extremal problems for plurisubharmonic functions

2005-09-20

arxiv.org/abs/math/0509454v4

Int. Math. Res. Not., Volume 2006, Art. ID 76283

Mathematics

Complex Variables

Final version, 26 pages

Scientific paper

We study properties of relative types of plurisubharmonic functions with respect to maximal plurisubharmonic weights. It is shown that they give a general form for upper semicontinuous, tropically additive functionals on plurisubharmonic singularities. We consider some extremal problems whose solutions are Green-like functions that give best possible bounds on a plurisubharmonic function, given the values of its types relative to some of (or all) the weights. An analyticity theorem is proved for the upperlevel sets for the types with respect to exponentially H\"older continuous weights, which leads to a result on propagation of plurisubharmonic singularities.

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