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arXiv · 1110.4011

Riemann surfaces out of paper

André de Carvalho·Toby Hall
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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.

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André de Carvalho, Toby Hall. 2011-10-18. Riemann surfaces out of paper. https://doi.org/10.1112/plms%2Fpdt020

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