A Fatou-Bieberbach domain intersecting the plane in the unit disk
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- by Erlend Fornæss Wold PDF
- Proc. Amer. Math. Soc. 140 (2012), 4205-4208 Request permission
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 $\mathbb D_z\subset \mathbb C_z$.References
- Erik Andersén, Volume-preserving automorphisms of $\textbf {C}^n$, Complex Variables Theory Appl. 14 (1990), no. 1-4, 223–235. MR 1048723, DOI 10.1080/17476939008814422
- Erik Andersén and László Lempert, On the group of holomorphic automorphisms of $\textbf {C}^n$, Invent. Math. 110 (1992), no. 2, 371–388. MR 1185588, DOI 10.1007/BF01231337
- P. G. Dixon and J. Esterle, Michael’s problem and the Poincaré-Fatou-Bieberbach phenomenon, Bull. Amer. Math. Soc. (N.S.) 15 (1986), no. 2, 127–187. MR 854551, DOI 10.1090/S0273-0979-1986-15463-7
- Franc Forstnerič, Noncritical holomorphic functions on Stein manifolds, Acta Math. 191 (2003), no. 2, 143–189. MR 2051397, DOI 10.1007/BF02392963
- Franc Forstnerič and Jean-Pierre Rosay, Approximation of biholomorphic mappings by automorphisms of $\textbf {C}^n$, Invent. Math. 112 (1993), no. 2, 323–349. MR 1213106, DOI 10.1007/BF01232438
- Franc Forstnerič and Erlend Fornæss Wold, Bordered Riemann surfaces in $\Bbb C^2$, J. Math. Pures Appl. (9) 91 (2009), no. 1, 100–114 (English, with English and French summaries). MR 2487902, DOI 10.1016/j.matpur.2008.09.010
- Josip Globevnik, On Fatou-Bieberbach domains, Math. Z. 229 (1998), no. 1, 91–106. MR 1649310, DOI 10.1007/PL00004653
- Jean-Pierre Rosay and Walter Rudin, Holomorphic maps from $\textbf {C}^n$ to $\textbf {C}^n$, Trans. Amer. Math. Soc. 310 (1988), no. 1, 47–86. MR 929658, DOI 10.1090/S0002-9947-1988-0929658-4
- Erlend Fornæss Wold, Embedding Riemann surfaces properly into $\Bbb C^2$, Internat. J. Math. 17 (2006), no. 8, 963–974. MR 2261643, DOI 10.1142/S0129167X06003746
Additional Information
- Erlend Fornæss Wold
- Affiliation: Matematisk Institutt, Universitetet i Oslo, Postboks 1053 Blindern, 0316 Oslo, Norway
- MR Author ID: 757618
- Email: erlendfw@math.uio.no
- 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
- © Copyright 2012 American Mathematical Society
- 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
- MathSciNet review: 2957210