Riemann surfaces out of paper

Details Riemann surfaces out of paper Riemann surfaces out of paper

2011-10-18

arxiv.org/abs/1110.4011v1

Mathematics

Complex Variables

36 pages, 11 figures

Scientific paper

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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