%0 Journal Article
%T Paper folding, Riemann surfaces, and convergence of pseudo-Anosov sequences
%A Andr¨¦ de Carvalho
%A Toby Hall
%J Mathematics
%D 2010
%I arXiv
%R 10.2140/gt.2012.16.1881
%X 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.
%U http://arxiv.org/abs/1010.3448v1