On hyperbolicity and tautness modulo an analytic subset of Hartogs domains

Details On hyperbolicity and tautness modulo an analytic subset of Hartogs domains On hyperbolicity and tautness modulo an analytic subset of Hartogs domains

2011-12-18

arxiv.org/abs/1112.4148v1

Mathematics

Complex Variables

10 pp

Scientific paper

Let $X$ be a complex space and $H$ a positive homogeneous plurisubharmonic function $H$ on $X\times\C^m$. Consider the Hartogs-type domain $\Omega_{H}(X):=\{(z,w)\in X\times \C^m:H(z,w)<1 \}$. Let $S$ be an analytic subset of $X$. We give necessary and sufficient conditions for hyperbolicity and tautness modulo $S\times \C^m$ of $\Omega_{H}(X)$, with the obvious corollaries for the special case of Hartogs domains.

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