Moving holomorphic disks off analytic subsets
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- by L. A. Campbell, A. Howard and T. Ochiai
- Proc. Amer. Math. Soc. 60 (1976), 106-108
- DOI: https://doi.org/10.1090/S0002-9939-1976-0425186-0
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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
- Robert Brody, Intrinsic metrics and measures on compact complex manifolds, Thesis, Harvard Univ., Cambridge, Mass., May 1975.
- L. Andrew Campbell and Roy H. Ogawa, On preserving the Kobayashi pseudodistance, Nagoya Math. J. 57 (1975), 37–47. MR 372258
- Mark Lee Green, Some Picard theorems for holomorphic maps to algebraic varieties, Amer. J. Math. 97 (1975), 43–75. MR 367302, DOI 10.2307/2373660
- Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker, Inc., New York, 1970. MR 0277770
- H. L. Royden, The extension of regular holomorphic maps, Proc. Amer. Math. Soc. 43 (1974), 306–310. MR 335851, DOI 10.1090/S0002-9939-1974-0335851-X
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- 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