Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

On ${\mathbf{R}}^{+}$ and ${\mathbf{C}}$ complete holomorphic vector fields

Author(s): Patrick Ahern; Manuel Flores; Jean-Pierre Rosay
Journal: Proc. Amer. Math. Soc. 128 (2000), 3107-3113.
MSC (1991): Primary 58F23; Secondary 32C10
Posted: March 2, 2000
MathSciNet review: 1664301
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Abstract | References | Similar articles | Additional information

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:

1.: P. Ahern and J.-P. Rosay, On Rebelo's theorem on singularities of holomorphic flows, to appear in Arkiv För Mat.
2.: E. Andersén and L. Lempert, On the group of holomorphic automorphisms of ${\mathbf C}^n$ , Invent. Math. 110 (1992) 371-388. MR 93i:32038
3.: G. Buzzard and J. E. Fornaess, Complete holomorphic vector fields and time 1 maps, Indiana Univ. Math. J. 44 (1996), no. 3, 539-546. MR 97f:32046
4.: F. Forstneric, Actions of $(\mathbf{R},+)$ and $(\mathbf{C},+)$ on complex manifolds, Math. Z. 223 (1996), 123-152. MR 97i:32041
5.: F. Forstneric and J. P. Rosay, Approximation of biholomorphic mappings by automorphisms of ${\mathbf C}^n$ , Invent. Math. 112 (1993) 323-349. MR 94f:32032

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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

DOI: 10.1090/S0002-9939-00-05321-1
PII: S 0002-9939(00)05321-1
Received by editor(s): November 20, 1998
Posted: 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 of article: Copyright 2000, American Mathematical Society

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