On ${\mathbf {R}}^{+}$ and ${\mathbf {C}}$ complete holomorphic vector fields
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- by Patrick Ahern, Manuel Flores and Jean-Pierre Rosay PDF
- Proc. Amer. Math. Soc. 128 (2000), 3107-3113 Request permission
Abstract:
We show that, on holomorphic manifolds that have a plurisubharmonic exhaustion function and that do not carry nonconstant bounded plurisubharmonic functions (e.g. ${\mathbf {C}}^{n}$), holomorphic vector fields that are complete in positive time are complete in complex time.References
- P. Ahern and J.-P. Rosay, On Rebelo’s theorem on singularities of holomorphic flows, to appear in Arkiv För Mat.
- 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
- Gregery T. Buzzard and John Erik Fornæss, Complete holomorphic vector fields and time-$1$ maps, Indiana Univ. Math. J. 44 (1995), no. 4, 1175–1182. MR 1386765
- Franc Forstneric, Actions of $(\mathbf R,+)$ and $(\mathbf C,+)$ on complex manifolds, Math. Z. 223 (1996), no. 1, 123–153. MR 1408866, DOI 10.1007/PL00004552
- 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
Additional Information
- Patrick Ahern
- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706-1388
- Email: ahern@math.wisc.edu
- Manuel Flores
- Affiliation: Department of Mathematics, University of La Laguna, La Laguna, Tenerife, Spain
- Email: mflores@anamat.csi.ull.es
- Jean-Pierre Rosay
- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706-1388
- Email: jrosay@math.wisc.edu
- Received by editor(s): November 20, 1998
- Published electronically: March 2, 2000
- Additional Notes: The second author was partially supported by a grant from DGESIC (Spain) PB95-0749-A
The third author was partially supported by a grant from NSF - Communicated by: Steven R. Bell
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3107-3113
- MSC (1991): Primary 58F23; Secondary 32C10
- DOI: https://doi.org/10.1090/S0002-9939-00-05321-1
- MathSciNet review: 1664301