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

Shulim Kaliman, M. Zaidenberg

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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 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.

Original languageEnglish (US)
Pages (from-to)661-672
Number of pages12
JournalTransactions of the American Mathematical Society
Volume348
Issue number2
StatePublished - 1996

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ASJC Scopus subject areas

  • Mathematics(all)

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