Riemann surfaces out of paper
Complex Variables
2014-02-26 v1
Abstract
Let S be a surface obtained from a plane polygon by identifying infinitely many pairs of segments along its boundary. A condition is given under which the complex structure in the interior of the polygon extends uniquely across the quotient of its boundary to make S into a closed Riemann surface. When this condition holds, a modulus of continuity is obtained for a uniformizing map on S.
Cite
@article{arxiv.1110.4011,
title = {Riemann surfaces out of paper},
author = {André de Carvalho and Toby Hall},
journal= {arXiv preprint arXiv:1110.4011},
year = {2014}
}
Comments
36 pages, 11 figures