- Tautness and Fatou components in 2
- Journal of Geometric Analysis
- Volume | Issue number
- 22 | 4
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
Hyperbolicity played an important role in the classification of Fatou components for rational functions
in the Riemann sphere. In higher dimensions Fatou components are not nearly as well understood.
We investigate the Kobayashi completeness and tautness of invariant Fatou components for
holomorphic endomorphisms of ℙ2 and for Hénon mappings. We show that basins of attraction and
domains with an attracting Riemann surface, previously known to be taut, are also complete, which is
strictly stronger. We also prove tautness for a class of Siegel domains.
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