### Abstract

We show that Thom's Transversality Theorem is valid for holomorphic mappings from Stein manifolds. More precisely, given such a mapping f : S → 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.

Original language | English (US) |
---|---|

Pages (from-to) | 661-672 |

Number of pages | 12 |

Journal | Transactions of the American Mathematical Society |

Volume | 348 |

Issue number | 2 |

State | Published - 1996 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Transactions of the American Mathematical Society*,

*348*(2), 661-672.

**A tranversality theorem for holomorphic mappings and stability of Eisenman-Kobayashi measures.** / Kaliman, Shulim; Zaidenberg, M.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 348, no. 2, pp. 661-672.

}

TY - JOUR

T1 - A tranversality theorem for holomorphic mappings and stability of Eisenman-Kobayashi measures

AU - Kaliman, Shulim

AU - Zaidenberg, M.

PY - 1996

Y1 - 1996

N2 - We show that Thom's Transversality Theorem is valid for holomorphic mappings from Stein manifolds. More precisely, given such a mapping f : S → M from a Stein manifold S to a complex manifold M and given an analytic subset A of the jet space Jk(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.

AB - We show that Thom's Transversality Theorem is valid for holomorphic mappings from Stein manifolds. More precisely, given such a mapping f : S → M from a Stein manifold S to a complex manifold M and given an analytic subset A of the jet space Jk(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.

UR - http://www.scopus.com/inward/record.url?scp=33645945015&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645945015&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33645945015

VL - 348

SP - 661

EP - 672

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -