Plurisubharmonic and holomorphic functions relative to the plurifine topology

Details Plurisubharmonic and holomorphic functions relative to the plurifine topology Plurisubharmonic and holomorphic functions relative to the plurifine topology

2010-11-19

arxiv.org/abs/1011.4472v1

Mathematics

Complex Variables

28 pages

Scientific paper

A weak and a strong concept of plurifinely plurisubharmonic and plurifinely holomorphic functions are introduced. Strong will imply weak. The weak concept is studied further. A function f is weakly plurifinely plurisubharmonic if and only if f o h is finely subharmonic for all complex affine-linear maps h. As a consequence, the regularization in the plurifine topology of a pointwise supremum of such functions is weakly plurifinely plurisubharmonic, and it differs from the pointwise supremum at most on a pluripolar set. Weak plurifine plurisubharmonicity and weak plurifine holomorphy are preserved under composition with weakly plurifinely holomorphic maps.

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