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A Fatou-Bieberbach domain intersecting the plane in the unit disk


Author: Erlend Fornæss Wold
Journal: Proc. Amer. Math. Soc. 140 (2012), 4205-4208
MSC (2010): Primary 32E30, 32H02
DOI: https://doi.org/10.1090/S0002-9939-2012-11267-5
Published electronically: April 4, 2012
MathSciNet review: 2957210
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Abstract: We construct a Fatou-Bieberbach domain $ \Omega $ in $ \mathbb{C}^2=\mathbb{C}_z\times \mathbb{C}_w$ such that one of the connected components of $ \Omega \cap \mathbb{C}_z$ is the unit disk $ \mathbb{D}_z\subset \mathbb{C}_z$.


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  • 1. Andersén, E.; Volume-preserving automorphisms of $ \mathbb{C}^n$. Complex Variables Theory Appl. 14 (1990), no. 1-4, 223-235. MR 1048723 (91d:32047)
  • 2. Andersén, E. and Lempert, L.; On the group of holomorphic automorphisms of $ \mathbb{C}^n$. Invent. Math. 110 (1992), no. 2, 371-388. MR 1185588 (93i:32038)
  • 3. Dixon, P. G. and Esterle, J.; Michael's problem and the Poincaré-Fatou-Bieberbach phenomenon. Bull. Amer. Math. Soc. (N.S.) 15 (1986), no. 2, 127-187. MR 854551 (88d:46090)
  • 4. Forstnerič, F.; Noncritical holomorphic functions on Stein manifolds. Acta Math. 191 (2003), no. 2, 143-189. MR 2051397 (2005b:32021)
  • 5. Forstnerič, F. and Rosay, J.-P.; Approximation of biholomorphic mappings by automorphisms of $ \mathbb{C}^n$. Invent. Math. 112 (1993), no. 2, 323-349. MR 1213106 (94f:32032)
  • 6. Forstnerič, F. and Wold, E. F.; Bordered Riemann surfaces in $ \mathbb{C}^2$. J. Math. Pures Appl. (9) 91 (2009), no. 1, 100-114. MR 2487902 (2010b:32008)
  • 7. Globevnik, J.; On Fatou-Bieberbach domains. Math. Z. 229 (1998), no. 1, 91-106. MR 1649310 (99g:32050)
  • 8. Rosay, J.-P. and Rudin, W.; Holomorphic maps from $ \mathbb{C}^n$ to $ \mathbb{C}^n$. Trans. Amer. Math. Soc. 310 (1988), no. 1, 47-86. MR 929658 (89d:32058)
  • 9. Wold, E. F.; Embedding Riemann surfaces properly into $ \mathbb{C}^2$. Internat. J. Math. 17 (2006), no. 8, 963-974. MR 2261643 (2007h:32027)

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Additional Information

Erlend Fornæss Wold
Affiliation: Matematisk Institutt, Universitetet i Oslo, Postboks 1053 Blindern, 0316 Oslo, Norway
Email: erlendfw@math.uio.no

DOI: https://doi.org/10.1090/S0002-9939-2012-11267-5
Received by editor(s): May 18, 2011
Received by editor(s) in revised form: May 20, 2011
Published electronically: April 4, 2012
Communicated by: Franc Forstneric
Article copyright: © Copyright 2012 American Mathematical Society

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