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On hyperbolicity and tautness modulo an analytic subset of Hartogs domains

Authors
  • Thai, Do Duc
  • Thomas, Pascal J.
  • Van Trao, Nguyen
  • Duc, Mai Anh
Type
Preprint
Publication Date
Dec 18, 2011
Submission Date
Dec 18, 2011
Identifiers
arXiv ID: 1112.4148
Source
arXiv
License
Yellow
External links

Abstract

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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