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Proceedings of the American Mathematical Society

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Moving holomorphic disks off analytic subsets


Authors: L. A. Campbell, A. Howard and T. Ochiai
Journal: Proc. Amer. Math. Soc. 60 (1976), 106-108
MSC: Primary 32H15
DOI: https://doi.org/10.1090/S0002-9939-1976-0425186-0
MathSciNet review: 0425186
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Abstract: Holomorphic maps of the unit disk into a complex manifold X, which miss an analytic subset A of codimension $ \geqslant 2$, are shown to be dense in all holomorphic maps of the disk into X. This implies that the Kobayashi pseudodistance on $ X - A$ is the same as that on X, and thus leads to some new examples of nonhyperbolic manifolds containing no lines.


References [Enhancements On Off] (What's this?)

  • [1] Robert Brody, Intrinsic metrics and measures on compact complex manifolds, Thesis, Harvard Univ., Cambridge, Mass., May 1975.
  • [2] L. Andrew Campbell and Roy H. Ogawa, On preserving the Kobayashi pseudodistance, Nagoya Math. J. 57 (1975), 37-47. MR 0372258 (51:8474)
  • [3] Mark Lee Green, Some Picard theorems for holomorphic maps to algebraic varieties, Amer. J. Math. 97 (1975), 43-75. MR 0367302 (51:3544)
  • [4] Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Appl. Math., Dekker, New York, 1970. MR 43 #3503. MR 0277770 (43:3503)
  • [5] H. L. Royden, The extension of regular holomorphic maps, Proc. Amer. Math. Soc. 43 (1974), 306-310. MR 0335851 (49:629)

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DOI: https://doi.org/10.1090/S0002-9939-1976-0425186-0
Article copyright: © Copyright 1976 American Mathematical Society

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