On indirect singular points for meromorphic functions

Transcendental Meromorphic Functions with Three Singular Values

Every transcendental meromorphic function f in the plane which has only three critical values satisfies lim inf r→∞ T (r, f) log r ≥ √ 3

Slow Escaping Points of Meromorphic Functions

We show that for any transcendental meromorphic function f there is a point z in the Julia set of f such that the iterates fn(z) escape, that is, tend to ∞, arbitrarily slowly. The proof uses new covering results for analytic functions. We also introduce several slow escaping sets, in each of which fn(z) tends to ∞ at a bounded rate, and establish the connections between these sets and the Juli...

Fixed-points and uniqueness of meromorphic functions

Let () () z g z f , be two nonconstant meromorphic functions, and let k n, be two positive integers with. 7 3 + ≥ k n If () () k n f and () () k n g share () z f z CM; and () z g share , IM ∞ then (1) () () z tg z f = for ; 2 ≥ k (2) either () () 2 2 2 1 , cz cz e c z g e c z f − = = or () () z tg z f = for , 1 = k where , , 2 1 c c and c are three nonzero constants satisfying () 1 4 2 2 1 2 − ...

Critical Points of Functions on Singular Spaces

We compare and contrast various notions of the “critical locus” of a complex analytic function on a singular space. After choosing a topological variant as our primary notion of the critical locus, we justify our choice by generalizing Lê and Saito’s result that constant Milnor number implies that Thom’s af condition is satisfied.

On Meromorphic Harmonic Functions with Respect to k-Symmetric Points