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arXiv · 2501.10595

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

Dmitrii Korikov
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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.

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Dmitrii Korikov. 2025-01-17. Determination of period matrix of double of surface with boundary via its DN map. https://doi.org/10.4153/s0008414x25000264

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