English

Lifts of Logarithmic Derivatives

Complex Variables 2025-10-28 v1

Abstract

Consider a sequence of meromorphic functions (fn)n(f_n)_n. This paper presents a technique that enables the transfer of convergence properties from (fn(m+1)/fn(m))n(f_n^{(m+1)}/f_n^{(m)})_n to subsequences of (fn(m)/fn(m1))n(f_n^{(m)}/f_n^{(m-1)})_n. As an application, we will show that the families of functions with bounded Schwarzian derivative are quasi-normal.

Keywords

Cite

@article{arxiv.2410.04839,
  title  = {Lifts of Logarithmic Derivatives},
  author = {Matthias Grätsch},
  journal= {arXiv preprint arXiv:2410.04839},
  year   = {2025}
}