Convex domains and Kobayashi hyperbolicity
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- by Theodore J. Barth PDF
- Proc. Amer. Math. Soc. 79 (1980), 556-558 Request permission
Abstract:
A geometrically convex domain in ${{\mathbf {C}}^n}$ is Kobayashi hyperbolic if and only if it contains no complex affine lines. This contrasts with an example of a nonhyperbolic pseudoconvex domain in ${{\mathbf {C}}^2}$ containing no (nonconstant) entire holomorphic curves.References
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- Mark L. Green, Holomorphic maps to complex tori, Amer. J. Math. 100 (1978), no. 3, 615–620. MR 501228, DOI 10.2307/2373842
- Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker, Inc., New York, 1970. MR 0277770
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 556-558
- MSC: Primary 32H20; Secondary 32F15, 32F99
- DOI: https://doi.org/10.1090/S0002-9939-1980-0572300-3
- MathSciNet review: 572300