Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Paper folding, Riemann surfaces, and convergence of pseudo-Anosov
  sequences   A method is presented for constructing closed surfaces out of Euclidean
polygons with infinitely many segment identifications along the boundary. The
metric on the quotient is identified. A sufficient condition is presented which
guarantees that the Euclidean structure on the polygons induces a unique
conformal structure on the quotient surface, making it into a closed Riemann
surface. In this case, a modulus of continuity for uniformizing coordinates is
found which depends only on the geometry of the polygons and on the
identifications. An application is presented in which a uniform modulus of
continuity is obtained for a family of pseudo-Anosov homeomorphisms, making it
possible to prove that they converge to a Teichm\"uller mapping on the Riemann
sphere.

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics