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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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