On hyperbolicity and tautness modulo an analytic subset of Hartogs domains

Thai, Do; Thomas, Pascal; Trao, Nguyen; Duc, Mai

doi:10.1090/S0002-9939-2013-11645-X

On hyperbolicity and tautness modulo an analytic subset of Hartogs domains
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by Do Duc Thai, Pascal J. Thomas, Nguyen Van Trao and Mai Anh Duc PDF

Proc. Amer. Math. Soc. 141 (2013), 3623-3631 Request permission

Abstract:

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

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