Affiliation:
1. Department of Mathematics, University of Houston, 4800 Calhoun Road, Houston, TX 77204, USA
Abstract
Motivated by the notion of the algebraic hyperbolicity, we introduce the notion of Nevanlinna hyperbolicity for a pair [Formula: see text], where [Formula: see text] is a projective variety and [Formula: see text] is an effective Cartier divisor on [Formula: see text]. This notion links and unifies the Nevanlinna theory, the complex hyperbolicity (Brody and Kobayashi hyperbolicity), the big Picard-type extension theorem (more generally the Borel hyperbolicity). It also implies the algebraic hyperbolicity. The key is to use the Nevanlinna theory on parabolic Riemann surfaces recently developed by P[Formula: see text]un and Sibony [Value distribution theory for parabolic Riemann surfaces, preprint (2014), arXiv:1403.6596].
Publisher
World Scientific Pub Co Pte Ltd
Cited by
2 articles.
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1. Further Results on Nevanlinna Hyperbolicity;The Journal of Geometric Analysis;2022-12-19
2. Nevanlinna theory via holomorphic forms;Pacific Journal of Mathematics;2022-08-28