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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A Tranversality Theorem
for Holomorphic Mappings and
Stability of Eisenman-Kobayashi Measures


Authors: Sh. Kaliman and M. Zaidenberg
Journal: Trans. Amer. Math. Soc. 348 (1996), 661-672
MSC (1991): Primary 32E10, 32H02, 58C10, 58A35, 58A07
MathSciNet review: 1321580
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that Thom's Transversality Theorem is valid for holomorphic mappings from Stein manifolds. More precisely, given such a mapping $f:S\rightarrow M$ from a Stein manifold $S$ to a complex manifold $M$ and given an analytic subset $A$ of the jet space $J^{k} (S, M), \; f$ can be approximated in neighborhoods of compacts by holomorphic mappings whose $k$-jet extensions are transversal to $A$. As an application the stability of Eisenman-Kobayshi intrinsic $k$-measures with respect to deleting analytic subsets of codimension $>k$ is proven. This is a generalization of the Campbell-Howard-Ochiai-Ogawa theorem on stability of Kobayashi pseudodistances.


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Additional Information

Sh. Kaliman
Affiliation: Department of Mathematics & Computer Science, University of Miami, Coral Gables, Florida 33124
Email: kaliman@paris-gw.cs.miami.edu

M. Zaidenberg
Affiliation: Université Grenoble I, Institut Fourier des Mathématiques, B.P. 74, 38402 Saint Martin d’Hères–Cédex, France
Email: zaidenbe@fourier.grenet.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01482-1
PII: S 0002-9947(96)01482-1
Received by editor(s): November 16, 1994
Additional Notes: Supported by General Research Support Award
Article copyright: © Copyright 1996 American Mathematical Society