On the behavior of meromorphic functions around some nonisolated singularities. II.
Ahlfors' disc theorem for Riemann covering surfaces is extended to normally exhaustible Klein coverings.
A general example of an analytic function in the unit disc possessing an exceptional set in Nevanlinna’s second fundamental theorem is built. It is used to show that some conditions on the size of the exceptional set are sharp, extending analogous results for meromorphic functions in the plane.
By using an extension of the spherical derivative introduced by Lappan, we obtain some results on normal functions and normal families, which extend Lappan's five-point theorems and Marty's criterion, and improve some previous results due to Li and Xie, and the author. Also, another proof of Lappan's theorem is given.
This paper studies the uniqueness of meromorphic functions that share two values, where , , . The results significantly rectify, improve and generalize the results due to Cao and Zhang (2012).