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Mathematics  2011 

Riemann surfaces out of paper

DOI: 10.1112/plms/pdt020

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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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