The Ahlfors estimate
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- by John Erik Fornæss PDF
- Proc. Amer. Math. Soc. 75 (1979), 95-98 Request permission
Abstract:
The Ahlfors estimate gives an upper bound on the growth of a complete Hermitian metric on the punctured unit disc, whose Gaussian curvature is bounded above by $- 1$. A. Sommese has obtained certain lower bounds on the growth as well. We answer two questions concerning lower bounds, raised by Sommese.References
- Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker, Inc., New York, 1970. MR 0277770
- Phillip A. Griffiths, Entire holomorphic mappings in one and several complex variables, Annals of Mathematics Studies, No. 85, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1976. The fifth set of Hermann Weyl Lectures, given at the Institute for Advanced Study, Princeton, N. J., October and November 1974. MR 0447638, DOI 10.1515/9781400881482
- Phillip A. Griffiths, Differential geometry and complex analysis, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Part 2, Stanford Univ., Stanford, Calif., 1973) Amer. Math. Soc., Providence, R.I., 1975, pp. 43–64. MR 0399521
- Andrew J. Sommese, Reversing the Ahlfors’ estimate, Proc. Amer. Math. Soc. 45 (1974), 242–244. MR 355117, DOI 10.1090/S0002-9939-1974-0355117-1
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 75 (1979), 95-98
- MSC: Primary 32H20; Secondary 30F30, 53B35
- DOI: https://doi.org/10.1090/S0002-9939-1979-0529222-5
- MathSciNet review: 529222