Weak normal and quasinormal families of holomorphic curves

Si Duc Quang and Dau Hong Quan

Address:
Si Duc Quang, Department of Mathematics, Hanoi National University of Education, 136-Xuan Thuy – Cau Giay – Hanoi, Vietnam and Thang Long Institute of Mathematics and Applied Sciences, Nghiem Xuan Yem, Hoang Mai, HaNoi, Vietnam
Dau Hong Quan, School of Natural Sciences Education, Vinh University, 182-Le Duan, Vinh, Nghe An, Vietnam

E-mail:
quangsd@hnue.edu.vn
hongquan19dhv@gmail.com

Abstract: In this paper we introduce the notion of weak normal and quasinormal families of holomorphic curves from a domain in $\mathbb{C}$ into projective spaces. We will prove some criteria for the weak normality and quasinormality of at most a certain order for such families of holomorphic curves.

AMSclassification: primary 30D35; secondary 32H02, 32H04, 32H30.

Keywords: weak normal, quasinormal family, holomorphic curve, meromorphic mappings.

DOI: 10.5817/AM2018-3-153