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Tautness and Fatou Components in ℙ2

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Abstract

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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Authors and Affiliations

  1. Korteweg de Vries Instituut voor Wiskunde, Universiteit van Amsterdam, P.O. Box 94248, 1090 GE, Amsterdam, Netherlands

    Han Peters

  2. Mathematics Department, University of Michigan, East Hall, Ann Arbor, MI, 48109, USA

    Crystal Zeager

Authors
  1. Han Peters
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  2. Crystal Zeager
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Correspondence to Han Peters.

Additional information

Communicated by Jeffrey Diller.

The first author was supported by a SP3-People Marie Curie Actionsgrant in the project Complex Dynamics (FP7-PEOPLE-2009-RG, 248443). The second author was supported by NSF RTG grant DMS-0602191.

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Peters, H., Zeager, C. Tautness and Fatou Components in ℙ2 . J Geom Anal 22, 934–941 (2012). https://doi.org/10.1007/s12220-011-9221-0

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  • DOI: https://doi.org/10.1007/s12220-011-9221-0

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