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  • On Fatou-Bieberbach domains
    Globevnik, Josip, 1945-
    A Fatou-Bieberbach domain is a domain in ▫$\mathbb C^2$▫ which is a biholomorphic image of ▫$\mathbb C^2$▫ and is not all of ▫$\mathbb C^2$▫. Let ▫$\Delta$▫ be the open unit disc in ▫$\mathbb C$▫ and ... let ▫$P=\Delta\times\Delta$▫ In the present paper we prove that there are Fatou-Bieberbach domains that satisfy: (1) Let ▫$Q\subset\mathbb C$▫ be a bounded open set with boundary of class ▫${\cal C}^1$▫ whose complement is connected. Let ▫$0<R<\infty$▫ be such that ▫$\overline{Q}\subset R\Delta$▫. There are a domain ▫$\Omega\subset\mathbb C^2$▫ and a volume-preserving biholomorphic map from ▫$\Omega$▫ onto ▫$\mathbb C^2$▫ such that: (i) ▫$\Omega \subset \{(z,w):|z|<{\rm max}\{R,|w|\}\}$▫, (ii) ▫$\Omega\cap RP$▫ is arbitrary small ▫${\cal C}^1$▫-perturbation of $▫Q\times R\Delta$▫. (2) Let ▫$0 < \gamma < \pi /2$▫ and let ▫$P=\mathbb C \setminus \{te^{i\theta}:t\ge 0, |\theta|\le \gamma\}$▫. There is a Fatou-Bieberbach domain ▫$\Omega$▫ such that ▫$\Omega \cap (P\times P)=0$▫.
    Vir: Mathematische Zeitschrift. - ISSN 0025-5874 (Let. 339, št. 1, 1998, str. 91-106)
    Vrsta gradiva - članek, sestavni del
    Leto - 1998
    Jezik - angleški
    COBISS.SI-ID - 8329049

    Povezava(-e):

    http://dx.doi.org/10.1007/PL00004653

vir: Mathematische Zeitschrift. - ISSN 0025-5874 (Let. 339, št. 1, 1998, str. 91-106)

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