Non-autonomous basins with uniform bounds are elliptic
HTML articles powered by AMS MathViewer
- by John Erik Fornæss and Erlend Fornæss Wold
- Proc. Amer. Math. Soc. 144 (2016), 4709-4714
- DOI: https://doi.org/10.1090/proc/12476
- Published electronically: July 21, 2016
- PDF | Request permission
Abstract:
We prove that a non-autonomous basin with bounds is an Oka manifold. A consequence is that it has an abundance of holomorphic maps from $\mathbb {C}^m$ into it, and in particular it does not carry a non-constant bounded plurisubharmonic function.References
- A. Abbondandolo, L. Arosio, J. E. Fornæss, P. Majer, H. Peters, J. Raissy, and L. Vivas, A survey on non-autonomous basins in several complex variables, http://arxiv.org/pdf/ 1311.3835.pdf
- John Erik Fornæss, Short $\Bbb C^k$, Complex analysis in several variables—Memorial Conference of Kiyoshi Oka’s Centennial Birthday, Adv. Stud. Pure Math., vol. 42, Math. Soc. Japan, Tokyo, 2004, pp. 95–108. MR 2087041, DOI 10.2969/aspm/04210095
- Franc Forstnerič, Stein manifolds and holomorphic mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 56, Springer, Heidelberg, 2011. The homotopy principle in complex analysis. MR 2975791, DOI 10.1007/978-3-642-22250-4
- Franc Forstnerič and Jasna Prezelj, Extending holomorphic sections from complex subvarieties, Math. Z. 236 (2001), no. 1, 43–68. MR 1812449, DOI 10.1007/PL00004826
- Hans Grauert, Holomorphe Funktionen mit Werten in komplexen Lieschen Gruppen, Math. Ann. 133 (1957), 450–472 (German). MR 98198, DOI 10.1007/BF01343758
- M. Gromov, Oka’s principle for holomorphic sections of elliptic bundles, J. Amer. Math. Soc. 2 (1989), no. 4, 851–897. MR 1001851, DOI 10.1090/S0894-0347-1989-1001851-9
Bibliographic Information
- John Erik Fornæss
- Affiliation: Department of Mathematics, Norwegian University of Science and Technology, 7491 Trondheim, Norway
- MR Author ID: 68145
- Erlend Fornæss Wold
- Affiliation: Department of Mathematics, University of Oslo, NO-0316 Oslo, Norway
- MR Author ID: 757618
- Received by editor(s): January 15, 2014
- Received by editor(s) in revised form: January 30, 2014
- Published electronically: July 21, 2016
- Additional Notes: The second author is supported by the NRC-grant 209751.
- Communicated by: Franc Forstneric
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4709-4714
- MSC (2010): Primary 32E30, 32H50
- DOI: https://doi.org/10.1090/proc/12476
- MathSciNet review: 3544522