On hyperbolicity and tautness modulo an analytic subset of Hartogs domains

Do Duc Thai (1) , Pascal J. Thomas (2) , Nguyen van Trao (1) , Mai Anh Duc (1)

1 DHSP - Laboratory of Complex Geometry
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Hartogs domains; complex spaces; Kobayashi hyperbolicity; taut spaces

Domaines: Variables complexes [math.CV]

Do Duc Thai, Pascal J. Thomas, Nguyen van Trao, Mai Anh Duc. On hyperbolicity and tautness modulo an analytic subset of Hartogs domains. Proc. Amer. Math. Soc., 2013, 141 (10), pp.3623-3631. ⟨hal-00728278⟩