Generalizations of Montel's normal criterion and Lappan's five-valued theorem to holomorphic curves

ABSTRACT

In this paper, we extend Montel's normal criterion to a family $\mathcal{F}$ of holomorphic mappings from a domain $\mathbb{D}$ of the complex plane $\mathbb{C}$ into a complex projective space ${\mathbb{P}}^n\left(\mathbb{C}\right)$ of dimension n. Furthermore, Lappan's five-valued theorem is extended to holomorphic curves.

COMMUNICATED BY:

• S. Krantz

KEYWORDS:

• Normal family
• normal mapping
• Nevanlinna theory

AMS SUBJECT CLASSIFICATIONS:

• Primary: 30D45
• 32H30

Acknowledgments

The authors wish to express thanks to the referee for reading the manuscript very carefully and making some suggestions towards the improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research results are sponsored by China/Shandong University International Postdoctoral Exchange Program, NSFC of Shandong [No. ZR2018MA014], PCSIRT [No. IRT1264] and The Fundamental Research Funds of Shandong University [No. 2017JC019].