Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation of conformal mappings by circle patterns   A circle pattern is a configuration of circles in the plane whose
combinatorics is given by a planar graph G such that to each vertex of G
corresponds a circle. If two vertices are connected by an edge in G, the
corresponding circles intersect with an intersection angle in $(0,\pi)$.
  Two sequences of circle patterns are employed to approximate a given
conformal map $g$ and its first derivative. For the domain of $g$ we use
embedded circle patterns where all circles have the same radius decreasing to 0
and which have uniformly bounded intersection angles. The image circle patterns
have the same combinatorics and intersection angles and are determined from
boundary conditions (radii or angles) according to the values of $g'$ ($|g'|$
or $\arg g'$). For quasicrystallic circle patterns the convergence result is
strengthened to $C^\infty$-convergence on compact subsets.

31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con