TY - JOUR

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

AU - Kaliman, Sh

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.

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U2 - 10.1090/s0002-9947-96-01482-1

DO - 10.1090/s0002-9947-96-01482-1

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 -