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Reversing the Ahlfors' estimate

Author: Andrew J. Sommese
Journal: Proc. Amer. Math. Soc. 45 (1974), 242-244
MSC: Primary 32H20
MathSciNet review: 0355117
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Abstract: It is shown that the Ahlfors' inequality for a complete Hermitian metric on the punctured disc with Gaussian curvature bounded below zero can be partially reversed for the averaged metric which is also complete and has the same curvature properties.

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  • [1] P. Griffiths, Periods of integrals on algebraic manifolds: Summary of main results and discussion of open problems, Bull. Amer. Math. Soc. 76 (1970), 228-296. MR 41 #3470. MR 0258824 (41:3470)
  • [2] S. Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Appl. Math., vol. 2, Marcel Dekker, New York, 1970. MR 43 #3503. MR 0277770 (43:3503)
  • [3] A. Sommese, Algebraic properties of the period mapping, Thesis, Princeton University, Princeton, N. J., 1973.

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Keywords: Ahlfors lemma, negative holomorphic sectional curvature
Article copyright: © Copyright 1974 American Mathematical Society

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