Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete uniformization of finite branched covers over the Riemann
  sphere via hyper-ideal circle patterns   With the help of hyper-ideal circle pattern theory, we have developed a
discrete version of the classical uniformization theorems for surfaces
represented as finite branched covers over the Riemann sphere as well as
compact polyhedral surfaces with non-positive curvature. We show that in the
case of such surfaces discrete uniformization via hyper-ideal circle patterns
always exists and is unique. We also propose a numerical algorithm, utilizing
convex optimization, that constructs the desired discrete uniformization.

29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph