Determination of period matrix of double of surface with boundary via its DN map

Abstract

As is well-known, a conformal class of a surface $M$ with boundary $\Gamma$ is determined by its DN map $\Lambda$. In the paper, the algorithm for determination of the $b$-period matrix $\mathbb{B}$ of the (Schottky) double of surface with boundary via $\Lambda$ is presented. Due to the Torelli theorem, $\mathbb{B}$ contains all information on the conformal class of $M$ except the proper way of attaching $\Gamma$ to it.