Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Ahlfors lemma and Picard's theorems   The article introduces Ahlfors' generalization of the Schwarz lemma. With
this powerful geometric tool of complex functions in one variable, we are able
to prove some theorems concerning the size of images under holomorphic
mappings, including the celebrated Picard's theorems. The article concludes
with a brief insight into the theory of Kobayashi hyperbolic complex manifolds.

19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph