Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A criterion of normality based on a single holomorphic function II   In this paper, we continue to discuss normality based on a single\linebreak
holomorphic function. We obtain the following result. Let $\CF$ be a family of
functions holomorphic on a domain $D\subset\mathbb C$. Let $k\ge2$ be an
integer and let $h(\not\equiv0)$ be a holomorphic function on $D$, such that
$h(z)$ has no common zeros with any $f\in\CF$. Assume also that the following
two conditions hold for every $f\in\CF$:\linebreak %{enumerate} [(a)] (a)
$f(z)=0\Longrightarrow f'(z)=h(z)$ and %[(b)] (b)
$f'(z)=h(z)\Longrightarrow|f^{(k)}(z)|\le c$, where $c$ is a constant. Then
$\CF$ is normal on $D$. %{enumerate}
  A geometrical approach is used to arrive at the result which significantly
improves the previous results of the authors, \textit{A criterion of normality
based on a single holomorphic function}, Acta Math. Sinica, English Series (1)
\textbf{27} (2011), 141--154 and of Chang, Fang, and Zalcman, \textit{Normal
families of holomorphic functions}, Illinois Math. J. (1) \textbf{48} (2004),
319--337.
  We also deal with two other similar criterions of normality. Our results are
shown to be sharp.

36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex