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

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- by Sh. Kaliman and M. Zaidenberg PDF
- Trans. Amer. Math. Soc.
**348**(1996), 661-672 Request permission

## 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.## References

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## Additional Information

**Sh. Kaliman**- Affiliation: Department of Mathematics & Computer Science, University of Miami, Coral Gables, Florida 33124
- MR Author ID: 97125
- 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
- MR Author ID: 196553
- Email: zaidenbe@fourier.grenet.fr
- Received by editor(s): November 16, 1994
- Additional Notes: Supported by General Research Support Award
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**348**(1996), 661-672 - MSC (1991): Primary 32E10, 32H02, 58C10, 58A35, 58A07
- DOI: https://doi.org/10.1090/S0002-9947-96-01482-1
- MathSciNet review: 1321580