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The Ahlfors estimate

Author: John Erik Fornæss
Journal: Proc. Amer. Math. Soc. 75 (1979), 95-98
MSC: Primary 32H20; Secondary 30F30, 53B35
MathSciNet review: 529222
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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.

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  • [1] S. Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Appl. Math., vol. 2, Marcel Dekker, New York, 1970. MR 0277770 (43:3503)
  • [2] P. Griffiths, Entire holomorphic mappings in one and several complex variables, Ann. of Math. Studies, no. 85, Princeton Univ. Press, Princeton, N.J., 1976. MR 0447638 (56:5948)
  • [3] -, Differential geometry and complex analysis, Differential Geometry, Proc. Sympos. Pure Math., vol. 27, Part 2, Amer. Math. Soc., Providence, R.I., 1975, pp. 43-64. MR 0399521 (53:3365)
  • [4] A. Sommese, Reversing the Ahlfors estimate, Proc. Amer. Math. Soc. 45 (1974), 242-244. MR 0355117 (50:7594)

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Keywords: Ahlfors lemma
Article copyright: © Copyright 1979 American Mathematical Society

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