Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperbolic metrics, homogeneous holomorphic functionals and Zalcman's
  conjecture   We show, using the Kobayashi and Caratheodory metrics on special holomorphic
disks in the universal Teichmuller space, that a wide class of holomorphic
functionals on the space of univalent functions in the disk is maximized by the
Koebe function or by its root transforms; their extremality is forced by
hyperbolic features. As consequences, this implies the proofs of the famous
Zalcman and Bieberbach conjectures.

18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph